đề toán thi thử lần 1năm 2015 trường cao bá quát

    !" Thời gian làm bài 180 phút ( không kể thời gian phát đề) #$: (2 điểm)    y x mx m= − + −  m    !"#$ m =  % " m  &' &(" !)* &("# !" +,)'(-). ,/ #$ (1 điểm)0123)(45        6   x x x x   − = − +  ÷    #$% (1 điểm)78&8$(9:;+$<=;41>) 2?)+ @ 2*)  A   x x xe y y x e = = = + :=)<=(B #$& (1điểm) 'CD)!)+ED)!)=)D)F). )G=6D)78:=H &6D) 2?.$D)I),+ 0123)(45 ( ) ( ) ( ) J      ) 6 )  )    x x x+ + − = #$ (1 điểm)7()$D))/:;KL1>)   5 C AP x y z+ + + = M123) (4LN=O'$8 R = PL1>)  P Q)=; 2*)(9  C '- R R H − − $8 6r =  #$' (1 điểm)7()L1>)/:;)ST' RUA - 2*)1- )()#)'S 6 R  M   −  ÷   - 2*)(9)+1)  R  I   −  ÷   % ". , VT #$( (1 điểm)4'1OST'+OS=D))' ; AB a=  AC a =  · A ABAC = WL1>)OT+ ;,)' A UA 78&8#$ '1OST$))X 2*)>)OTSQ a  #$) (1 điểm)0123)(45 ( ) ( )   6  C C 6 C x x x x x x x− − + = − − − ∈¡ #$* (1 điểm)Y23)74)("ZH#&=[ 6   6    6  6 b c a c b c P a b a c + + − = + + + \\\\\\\\\\\\\\\\\\\\\\\\\\\\\]^7\\\\\\\\\\\\\\\\\\\\\\\\\  #$ +,-$./012345 ,67 #$ 89:; <= 89:;  m = 'Y+)   J 6y x x= − + _7`1: " D = ¡ _        J 6 R    J 6 x x x x y x x y x x →−∞ →−∞ →+∞ →+∞ = − + = +∞ = − + = +∞ 9 _ 6 a  Uy x x= − A 6 a A  6 x y y x y = ⇒ =  = ⇔  = ± ⇒ = −   : −∞ \A +∞ ;b \A_A\A_ ; +∞ 6 +∞ \6 \6  9 _  ]    !)    (  $)  ( ) ( ) RA R− ∪ + ∞    )"    (  $) ( ) ( ) R  AR−∞ − ∪  _] + ++ A 6 CÐ x y= = ] +&=+  6 CT x y= ± = − 9 c& Ld ( ) ( ) ( ) ( ) ( ) 6R  R 6  AR6  R 6  6R 6− − − − −  c!"5 9 3= 89:; 7' 6   A a      A x y x mx x x m x m =  = − = − = ⇔  =  ]'6 &(" a Ay⇔ = '6)d1-d ay  eYH=$: <= )d ' Am ⇔ > 9  '6 &("# !"5 ( ) ( ) ( )   AR   R   R A m B m m m C m m m− − − + − − + − ( )  R OB m m m⇒ = − − + − uuur R ( )  RAC m m= − uuur 9 M4T :[)<=/;T=D=D))'/S f '/(-)ST$V$  AOB AC = uuur uuur     Am m m m⇒ − − − + − = 9 ( ) 6   Am m m m⇔ − + − + = ( ) ( )  A   A  m m m m m =  ⇔ − + = ⇔  =  Ocg)("N4 9 #$ 0123)(45        6   x x x x   − = − +  ÷    89:; ch=$d5 ( )  Ax x k k π ≠ ⇔ ≠ ∈¢ 9 ( )      6       x x x x x x − − +   ⇔ =  ÷   ( ) ( ) ( )          x x x x⇔ − = − − ( ) ( )        Ax x x⇔ − − + = 9         A x x x  =  ⇔  − + =     U  C   U x k x k x k π π π π  = +  = ⇔ ∈   = +   ¢ ( )       A      Ax x x x− + = ⇔ + − = ( )  A       x k x k x x k π π π π  = +  =   ⇔ ⇔ ∈   =   = +   ¢ D)d 9 O h=$d')d#123)(45 ( )  U C  U x k k x k π π π π  = +  ∈   = +   ¢ 9 #$% 89:; 7' A A  x x xe x e = ⇔ = + =;(41>) i4)) 2?)+@  2*)  A A   x x xe y y x x e = = = = + f '&8$(9:; ( )   A   x x xe V dx I e π π = = + ∫ 9 cL ( )     x x x u x du dx e dv dx v e e =  =    ⇔   = = −   + +   9    A A A       x x x x x dx e I dx e e e e   − − ⇒ = + = + −  ÷ + + + +   ∫ ∫  ( )   A A         x e e x e e e − + = + − + = − + + 9     e e V e π +   ⇒ = −  ÷ +     9 #$& 89:; <;>2?"@A$B/ 9 'CD)!)+ED)!)=)D)F).)G= 6D)78:=H &6D) 2?.$D)I),+ 0.ST23)[)6j. 2?D)!)+kj. 2? D)!)=)kj. 2?D)F)k ]j. 2?D)I)+kST D,:=)$P H A B C= È È glm]gmS_mT_m 3 5 3 16 C 10 P(A) 560 C = =   3 7 3 16 C 35 P(B) 560 C = =  3 4 3 16 C 4 P(C) 560 C = =  49 7 P(H) 560 80 = =  9 T.D)$D)I)+ H  7 73 P(H) 1 P(H) 1 80 80 = - = - =  9 ch=$d5 A  x x >   ≠  m ( ) ( )    ) 6 )  ) x x x⇔ + + − = ( ) ( )   ) 6  ) x x x ⇔ + − =   9 ( ) 6  x x x⇔ + − = ( ) ( ) ( ) ( ) 6   6   x x x x x x  + − = ⇔  + − =      6 A U 6 A x x x x  − − = ⇔  + − =  R 6 6  6 x x x = − =  ⇔  = − ±  O h=$d')d#123)(4 6R 6  6x x= = − + 9 #$ 89:; WL1>)m'Q311=; ( ) RRn = r 0. ( ) ∆  2*)>)<=]=D))'L1>)m4 ( ) ∆ ` n r Q3V 123) m23)(4 2*)>) ( ) ∆ 'Y+)    x t y t z t = +   = − +   = − +  9 0.n-LN=O4 I ∈∆ =;( ( )  R  R I t t t+ − + − + 7'   U 6 6IH R r= − = − = 9 WL$ ( ) ( ) ( )  R R 6 6   6  AR 6R C6 t I t d I P IH t I  = ⇒ − − = ⇔ = ⇔  = − ⇒ − −   9 M`;'LN=N45 ( ) ( ) ( ) ( ) ( )           5   6 U   5 6  U S x y z S x y z − + + + + = + + + + = 9 #$' 89:; 0. 2*)(9)+1)STo$8#' C C C RC   IA R IA   = ⇒ = =  ÷   uur m23)(4 2*)(9'Y+) ( )    C    x y   + + − =  ÷   9 m23)(4 2*)>)SW'Y+)  Ax − = 0.  D AM C= ∩ 4. ,#fZid123)(4 ( ) ( )     A   C   C   x x x y y − =  =    ⇔     + + − = − =   ÷       U x y =  ⇔  =  . ,# &S; ( )  R   x D y =  ⇒ −  = −  9 fSW 2*)1-)()#)'Sf &8)X#=) » BC =;( BC ID ⊥ c2*)>)T <= &W` C R C  ID   = −  ÷   uur Q311=;'123) (4 ( ) C 6  C A  C A   x y x y   − − + = ⇔ − − =  ÷   9 7. ,#T)d#d123)(4 ( )     C A  C  C  A    x y x y y y x y − − =  = +   ⇔     + = + + − =   ÷     C 6 A  x x hay y y = = −   ⇔   = = −   M`; ( ) ( ) ( ) ( ) CRA  6R  6R   CRAB C hay B C− − − − 9 #$( 89:; >2/26/>@2@C<D2E,@2FGH= 89:; 7())ST$p 2*)S]'      BC AH BC SAH BC SA do SA ABC ⊥  ⇒ ⊥  ⊥ ⊥  BC SH ⇒ ⊥ O=;()')XL1>)  SBC   ABC  · A UASHA = q1YB) "8D())ST'    A     A      E  BC AB AC AB AC a a a a a = + −   = + − − =  ÷   EBC a⇒ = 9 fd8)ST  A   6 6  A       ABC a S AB AC a a ∆ = = = WL$    ABC S BC AH ∆ =   6  E E ABC S a a AH BC a ∆ ⇒ = = = M`;&8$'1OST  6    6 6 E     6 6  E  S ABC ABC a a a V S SA ∆ = = =   9 >2D2!I.@"@2.,J<2<,:KL./2M.HN4 89:; f)44STf' r r AC SBD  ( ) ( ) ( )     d AC SB d AC SBD d A SBD= = $p  AK BD K BD⊥ ∈ '   BD AK BD SAK BD SA ⊥  ⇒ ⊥  ⊥    BD SBD⊂     SBD SAK⊥ Q)=;O ())OS$p 2*)Sn4 ( ) AI SBD⊥ ( ) ( ) d A SBD AI⇒ = 9 7)ST=D)+' · A UAABK =  A 6  UA  a AK AB= = 7)OS=D)+S'          E  s 6 s s 6 s s a AI AI SA AK a a a = + = + = ⇒ = M`; ( ) 6 s  s a d AC SB AI= = 9 #$) 0123)(45 ( ) ( )   6  C C 6 C x x x x x x x− − + = − − − ∈¡ 89:; ch=$d A Cx≤ ≤ T e123)(423) 23)5 9 ( ) ( )    C 6  C   C Ax x x x x x− − − − + − + = cL  C    Au x v x u v= − = ≥ $ '123)(4(@5 ( )   6   Au uv v u v− − + + = ( )   6    Au v u v v⇔ − − + − = ( ) ( ) ( )     6        u v v v v v v∆ = − − − = + + = +  ' 6     v v u v − + + = = L 6     v v u v − − − = = − 9 M u v= $ '    C  C   C Ax x x x x x− = ⇔ − = ⇔ + − =   s  sx hay x⇔ = − + = − − + M u v= − $ '  C  tx x− = − 9 M  h=  $d5  A C  C  U  Ax x≤ ≤ ⇒ − ≤ − < − =   123)  (4  t D )d M`;123)(4')d5  sx⇔ = − + 9 #$* 7407uu#&=[ 6   6    6  6 b c a c b c P a b a c + + − = + + + 89:; 7' 6 6  6      J  6  6 b c a c b c P a b a c + + −       + = + + + + +  ÷  ÷  ÷ +        ( )     6 6  6  6 a b c a b a c   = + + + +  ÷ +   9 M.  Ax y > '    x y x y + ≥ + c>)[:;($ Ax y= > q1YB)H >)[( 2?     6  6a a a b + ≥ +   U  6  6  6 6a b a c a b c + ≥ + + + + 9 O=;(    U  6  6  6 6a b a c a b c + + ≥ + + + f '  U CP P + ≥ ⇔ ≥ 9 M`;  CP =  + 2?$  6 6 Aa b c= = > 9 7v7/qu 7owxu07]m7S/Tqyzq7\yuc{7]n7]|7]m7yz}0nSu~WAC Wvu7/qu Thời gian làm bài 180 phút ( không kể thời gian phát đề) -=(2điểm):2!247AE    x y x + = − <;O2I!A"/AP3,Q/2,RN4NS:T/2U@C<247AE 3;17.,"/0U2V2B/@C<7A<!@2!/T/W,>/2B/7+/:,67 ( ) M C∈ 74/,QG /$5Q/W, M @C< ( ) C /W!NX,2<,/0Y@/Z<:+7+//<7.,"@@F/0Z./#7[7/0R :KL./2M.  y m= − Câu 2 (1điểm) Giải phương trình   s 6  6   C 6 A   x x x x π   − + − − + =  ÷    -=681điểm).>2/>@2G2# 6    A  = + + ∫ x dx I x x -=(1điểm).<;17AEG2\@]/2V<7^ ( ) ( )    6   Az z z+ − + + =  `1?1 { } 6CE = 0.W`1?1-'8H6X X D,$==,•€H;)G=,=,W78: =H &e)X# '•)A #$  (1điểm)7()  $D)  )  @  d   .  ,  /:;K        6  & ( ) ( ) ( ) RRA  ARRA  ARR A B C −  2*)>)     5   6 x y z d − + − = = €`1123)(4 2*) >) ∆ =D))'L1>)  ( ) ABC  P 2*)>) d + & D  &   A B C D +,[Yd'&8•) s U #$'(1điểm)7()d. , /:;  2*)(9 ( ) ( ) ( )   5   C x y− + − =  2*) >)   5  A 5  Ad mx y m d x my m+ − − = − + − = 74 &‚ 2*)>)   d d P ( ) C + &1-d) & '[)'Yd8H Câu 7(1 điểm). 4'1OSTf' ;STf4=D)OSg =D))'L1>)STWuN2?(=) &Sff0')XL 1>)OTWL1>)ST•)C A 78&84'1OSTuW$) ƒf L1>)OTW #$) (1điểm).Gd123)(4 ( ) 6 U U  U   6   C y x y x x y x  + =   + =   #$*(1điểm)Y23)Zi ( )    sa b c a b c   + − + − =  ÷   [)(•)5 ( )          6JACa b c a b c   + + + + ≥  ÷   _ `  _ #$ 8=:; <;=: 7%c5  „  D R   =       ( ) r  6   y x − = −  x D∀ ∈ ])"($)    R R R    −∞ +∞  9 0+5        x x y y − +     → →  ÷  ÷     = −∞ = +∞    x = d` [)     x x y y →−∞ →+∞ = =    y = d`)) 9 T)5 % \    _  ;a \  \ ;   _  \     9 c!"5 9 3;=:  m1=;+ ( ) A A M x y  ( ) ( ) A A  A 6   y x x y x = − − + − 9 0.ST) &#1=;(B(B=)23)[) u ( )  A A  A      B x x y x + − = − (.)-0#)/ST' ( )  A A  A    6   G x x y x + − = − 9 7Q)'•( 2*)>)  y m= −  ( )  A A  A      6   x x m x + − = − − 7+' ( ) ( ) ( ) ( )     A A A A A    A A A U      U         x x x x x x x x − − + − = = − ≥ − − − − 9 [...]... tròn ( C ) có tâm I ( 1; 2 ) và có bán kính R = 2 u r u u r uu r u r Véc tơ pháp tuyến của d1 , d 2 lần lượt là n1 = ( m;1) , n2 = ( 1; −m ) ⇒ n1.n2 = 0 ⇒ d1 ⊥ d 2 0,25 Gọi A,B là giao điểm của d1 với ( C ) ,C,D là giao điểm của d 2 với ( C ) (A,B,C,D theo thứ tự trên đường tròn) h1 , h2 lần lượt là khoảng cách từ I đến d1 , d 2 m 1 < R, h2 = < R nên d1 , d 2 luôn cắt ( C ) tại 2 điểm phân...Vậy để tồn tại ít nhất một điểm M thỏa mãn điều kiện bài toán thi 2m − 1 ≥ Câu 2 (1.0đ) −1 1 ⇔m≥ 3 3 Phương trình đã cho tương đương: π + k 2π 2 Kết hợp (1) và (2), ta có: x = 1 x 3dx 0 x 2 + x 4 +1 I =∫ 0,25 π   x = 6 + k 2π ⇔  x = 5π + k 2π  6  ( 2) .    !" Thời gian làm bài 180 phút ( không kể thời gian phát đề) #$: (2 điểm)    y x mx m= − + −  m   . > 9 7v7/qu 7owxu07]m7S/Tqyzq7yuc{7]n7]|7]m7yz}0nSu~WAC Wvu7/qu Thời gian làm bài 180 phút ( không kể thời gian phát đề) -=(2điểm):2!247AE    x y x + = − <;O2I!A"/AP3,Q/2,RN4NS:T/2U@C<247AE 3;17.,"/0U2V2B/@C<7A<!@2!/T/W,>/2B/7+/:,67 (