Đề+ĐA môn toán thi Thử ĐH lần 2

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E) ^*,/"2/.:P*;<2#%<*".aX5FI*+."=.P*"0M"].! Câu IV (1 đim).7$$,=E].C">N9.:7"%<K*+9"5F$ '   ( ) ( ) x m x m x+ ≥ + + − + ! bMỗi thí sinh chỉ chọn câu Va hoặc Vb Câu Va (3 đim)!Chương trình cơ bản ! :9$_.C"@9.c<,WOLH*",5=$('G)2#"<5,>?9."@9*+C">N9.:7"0#     d x y− + = 2#    ' d x y+ − = !d5J.C">N9.:7",>?9."@9,5SK<2#.B2M5"<5,>?9 ."@9   #d v d $W..<$95**D*+,e"0#95<,5=$*;<   #d v d ! ! :94"995<2M5"F.c<,WOLfH*""<5,>?9."@9         x y z− + − ∆ = = −    '     x y z+ − − ∆ = = − 2#$_.*`K( )O  gL  gf  ghOiLgjfgk6!d5J.C">N9.:7"$_. C"@9.5JCOl*2M5$_.*`K( ),-9."?5%9%92M5  ∆ 2#  ∆ ! '! 7$C"`."m**;<%&C"a* ( ) n  i− Câu Vb. (3 đim).Chương trình nâng cao ! :9$_.C"@9.c<,WOLH*""LCoE0 ( )H *+C">N9.:7"      x y a b − = 2#0#,5=$E].4p ."KW*()!c5X  HX  0#**,>?9."@9,5SK<2#%9%92M5**,>?9.5F$*Q*;<()! "a9$5":q9"7"E7""#".BET5X  HX  2#**,>?9.5F$*Q*;<()*+X5F.P*"4"9,r5! ! :94"995<2M5"F.c<,WOLfH*"',5=$(G'Gi)HI(GG)H(GG)!7$.c< ,W*;<,5=$%<*"  gI  g  ,B.95.:/"s"].! '! 515E].C">N9.:7"  h Hk  j 09 h09 h 09x x x+ ≤ − tJ.t (EW*5."54"99515."P*"97."\$) uuv DK w W5XK9 5=$     ^x6 ¡ mE5J."5\Ly6'O  gjOg'6'(Og)    x ≥ ∀ ∈ ¡ #$%&,-9E5J.:\ ¡ #$%&4"9*+*m*.:/ 5M5"B 05$ x y →±∞ = ±∞ I19E5J."5\ O −∞  +∞ Ly gg L +∞ −∞ -."/ L  i O k ' k k   ">N9.:7""#",W95<,5=$*;<,-."/( $ )2#,>?9."@9L6Og O ' g'O  g$O6   '  x x x m =  ⇔  + + =  >?9."@9L6Og*A.,-."/( $ ).B5',5=$C"DE5F.4"52#*"e4"5   ( ) ' g x x x m= + + = *+"<59"5F$C"DE5F.4"*4"52#*"e4"5  n  n h  h ()    m m g m m  ∆ > − > <    ⇔ ⇔    ≠ ≠    ≠  (z) "5,+"#",W*;<I2#."s<${ ' ! B C B C x x x x m + = −   =  () <*+|y(O)6'O  gjOg$g F%&9+***.5JC.KLJ.B5I2#0#|y(O I )6  ' j  B B x x m+ + + H|y(O  )6  ' j  C C x x m+ + +  *.5JC.KLJ.B5I2#2K99+*4"52#*"e4"5|y(O I )!|y(O  )6i ⇔ (  ' j  B B x x m+ + + )!(  ' j  C C x x m+ + + )6i ⇔ (  ' j B B x x+ )(  ' j C C x x+ )g($g)(  ' j B B x x+ g  ' j C C x x+ )g($g)  6i ⇔   n( ! ) } ( ) 'j '( )(( )  ( )) 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+ + + + + + − + + g$  g$g6 J."~C2M5().<,>~* n$  •kh$g'j$g'($g)(n•$i')g$  g$g6 ⇔ h$  •'$g6C">N9.:7"29"5F$! dQL4"9*+95.:/*;<$."s<${L\K*`K! k k k k     5€K45F  'H 'x y≤ ≤ ≤ ≤ <*+ ' ' ' ' x y y x  + − =   + − =   ⇔  (' )   (' )  x y x y y x y x  − + − =   − + − =   (' ) (' )  (' )  (' )  x y y x x y y x ⇒ − + − = − =  ⇔  − =  ⇔   ' ' x y x y  =    =    =    =    5=$.:<.<."]L  ' H  ' x x y y = =     = =   ."s<${! J.0KQF*+"F*+"<59"5F$  ' H  ' x x y y = =     = =   k k k k   4 %5O *% *%  x x ≠   ≠  ! ">N9.:7".>N9,>N92M5   ( %5O)  *% ( %5O)  *% % %5O *%  %5 %5O *%   *% (%5O *% ) ( %5O)( *% )  %5O %5O *% %5O *% %5O!*%   (%5O )(*% )  %5O  *%  x x c x x x x x x x x x x x x − − − − = ⇔ = − − − − ⇔ = ⇔ − = + − + − ⇔ − + − = ⇔ − + = =  ⇔  = −  g)%5O64"9."s<${4274"5,+*%O6! g)*%O6i  Hx k k π π ⇔ = + ∈¢ ."s<${! J.0KQ">N9.:7"*+"c9"5F$  Hx k k π π = + ∈¢  k k k k     >?9.:R.D$(G)E4P"U6*+C">N9.:7"(Oi)  g(Li)  6 5€K45F  'x≤ ≤ !•C">N9.:7",>?9.:R.<*+    ( )y x= + − − 2M5 y ≥ d#    ( )y x= − − − 2M5 y < ! "=.P*"2Q.."=*`.7$  ( ) ( ) ' '       '     ( )   ( ) }  ( ) V x dx x dx x dx π π π = + − − − − − − = − − ∫ ∫ ∫ _.O•6%5.2M5   x π π − ≤ ≤ ! k k O6 ⇒ .6  π − O6' ⇒ .6  π XO6*%.X.H   ( )x− − 6*%.! dQLd6    } %c tdt π π π − ∫ 6    h ( % ) hc t dt π π π π − + = ∫ k k   <) c50#.:K9,5=$*;<! <*+ HBN AB BN AM BN BM⊥ ⊥ ⇒ ⊥ O X,+.<$95*I2K9.B5I%KL:<I6  MN H   .>N9.m6  MN ! dQL6I666  MN 6  b  D$$_.*`K9B5.5JC0#HE4P"U6  b I E)_.6OYHI6LY  <$95*I2K9.B5I\  6I  gI  L <$95*2K9.B5\  6  g  KL:<E  6  6  gI  gI  6O  g<  gL   x,+O  gL  6E  •<  4"9,r5! aX5FI*+,L0#IH,>?9*<I! "=.P*"        <O ( ) ( ) j   V y a x y a b a= ≤ + = − ! "=.P*".aX5FI0M"].4"56I6    b a− ! k k k k d  <*+ '   ( ) ( ) x m x m x+ ≥ + + − +    ( )( ) ( ) ( )x x x m x x x⇔ + − + ≥ − + + + 5€K45F x ≥ − "5,+E].C">N9.:7".>N9,>N92M5       x x m x x x x + + ≥ + − + − +  ⇔       x x m x x x x + + − ≥ − + − + (z) _..6    x x x + − + HE].C">N9.:7"(z)*+XB9.•.   m≥ () <*+       ‚ H ‚   '  ( )  x x t t x x x x x x − − + = = ⇔ = − + + − + − + ! I19E5J."5\ k O i  '− +  +∞ .y g i .  '  ' ' +    dQL  ƒ ' G ' t   +   ∈     !I].C">N9.:7",{*"*+9"5F$4"52#*"e4"5()*+9"5F$  ƒ ' G ' t   +   ∈     4"52#*"e4"5  ƒ ' „G … ' <O ( ) t M f t m + ∈ ≥ 2M5|(.)6.•.  |y(.)6•. I19E5J."5\ .     '  ' ' + |y(.) g i |(.)   h •E19E5J."5\  ƒ ' „G … '   <O ( ) h  t M f t khi x + ∈ = = dQLL*E..>N9,>N92M5  h m ≤ k k k d< '   >?9."@9,5SK<('G)*+XB9  <O ' by a b∆ + − − = >?9."@9 ∆ .B2M5"<5,>?9."@9   #d v d $W..<$95**D*+,e"0#95<*;<   #d v d 4"52#*"e4"5   ( H ) ( H )d d∆ = ∆    %( HX ) %( HX )c c⇔ ∆ = ∆        k( ) k( )   a b a b a b a b a b a b − + ⇔ = + + ⇔ − = +   a b a b ⇔ − = + "_*  a b a b − = − −  ' a b⇔ − = "_* ' a b+ = "c<6'HE6"_*<6HE6i'! dQL*+"<5,>?9."@9."s<${L\K*`KE#5.'OgL•62#O•'L6 k k k k   do*.N*"eC">N9*;<         x y z− + − ∆ = = − 2#    '     x y z+ − − ∆ = = − 0`0>~.0# (G G)H ( GG)u v= − = − r r !_.C"@9()%9%92M5  ∆ 2#  ∆ "Q*_C2o*.N k (G G)H ( GG)u v= − = − r r 0#$*_C2o*.N*"eC">N9! <*+ ( )       G G 'G jG '(GG)       n   − − = = − − = −  ÷ − −   r !_.C"@9()*+XB9 ()OgLg$6! _.*`K( )*+.D$(iGGi')2#E4P"U6'! _.C"@9().5JCOl*2M5( )4"52#*"e4"5      ( H( )) ' ' k    m d I P R m − + + = ⇔ = ⇔ = ± + + dQL*+"<5$_.C"@9."s<${L\K*`K0#OgLg ' k 62#OgL• ' k 6! k k k '  <*+ ( ) ( ) ( ) h n  h h h h   ( ) (  ) ( )  ( )   i i i i i i i − = − − = − − = − = −  dQLC"`."m**;<%&C"a*.:\0# h  k k k k dE '   *,>?9.5F$*Q*;<()*+XB9 b y x a = ± !c5(O  GL  )       ( )  x y H a b ∈ ⇒ − = () *,>?9."@9X  GX  *+C">N9.:7"0#     # b b b b y x y x v y x y x a a a a = + − = − + +  *95<,5=$*;<X  GX  2M5**,>?9.5F$*Q(     G     x y a b y x b a + + )HI(     G     x y a b y x b a − − )! x5F.P*""7"E7""#" 6 I 6!I!%5 AOB ∠ 6    ! ( ! )OA OB OAOB− uuur uuur uuur uuur <*+   !OA OB uuur uuur 6             (( ) ( ) )(( ) ( ) )         x y x y a b a b y x y x b a b a + + + − + − 6           ( ) h x y a b a b   + −  ÷   6    h a b   +  ÷   (."o())  ( ! )OA OB uuur uuur 6          (( )( ) ( )( ))         x x y y a a b b y y x x b b a a + − + + − 6           ( ) h x y a b a b   − −  ÷   6    h a b   −  ÷   (."o()) x,+  ab S = 4"9,r5! k k k k   c<,W.:c9.D$.<$95*I0#(GG) <*+ k k  ( ) ( ) ( )                   I  ' ( ) ' MG GA MG GB MG GC MG GA GB GC MG GA GB GC MG GA GB GC GA GB GC + + = + + + + + = + + + + + + = + + + ≥ + + uuuur uuur uuuur uuur uuuur uuur uuuur uuur uuur uuur dQL  gI  g   ≥    GA GB GC+ + X]KEq9O1L:<4"52#*"e4"5 M G ≡ k k '  <*+  ( ) h j  h  Hk  j Hk    h Hk  j           h 09  09 h09 h 09 09 h09  09 h09 h 09 h 09  09 09  09 09 j }09 09  x x x x x x x x x x x x x x x x x  − ≥   + ≤ − ⇔ + ≥   + ≤ −   − ≥   + ≥  ⇔  + ≤ − +   >     } k }  09 k 09       h x x x x x   ≤ ≤     ⇔  ≤ −     >   ≤ ≤  ⇔  < ≤   QC9"5F$*;<E].C">N9.:7"0# 6 } k  „G … (G … h ∪ k k k k   . :94"995<*""<5,5=$HI*&,/"H,WX#5,BI6<Y!O 2# IL0#"<5Z< ,>?9."@92K99+*2M5"<K 2# *[92K99+*2M5I!:O 2# IL0]L"<5,5=$ 2# %< *"6E(2M5E0#$W.%&*".:>M* 2# EY<)! <). + *A.,-."/( $ ).B5',5=$C"DE5F.(G)HIH %<*"**.5JC.KLJ*;<( $ ).B5I 2# 2K99+*2M5"<K! Câu II (2 đim)! 1. 515"FC">N9.:7" ' ' ' ' x y y x  + − =   + − =   2. 515C">N9.:7"  . :94"995<*""<5,5=$HI*&,/"H,WX#5,BI6<Y!O 2# IL0#"<5Z< ,>?9."@92K99+*2M5"<K 2# *[92K99+*2M5I!:O 2# IL0]L"<5,5=$ 2# %< *"6E(2M5E0#$W.%&*".:>M* 2# EY<)! <) ^*,/".D$ 2# E4P"$_.*`K9B5.5JC.aX5FI! E) ^*,/" 2/ .:P*;< 2# %<*".aX5FI*+."=.P*"0M"].! Câu