Bộ đề&đáp án ĐH-CĐ Toán 2010-2011./.

   !"#$%(không kể thời gian phát đề) &'()*+,-./0123 45-/0123       !!"#$%&'(  )*#+#$%&',-./#+0123#4      5'6 #78(29          :+ + < 45-/0123  ;0<=>-*       :    '   π   + + +  ÷   = +  ;?0<=>-*9         − ≥ − − + 45-/0123 )@@019       A  B  B C D  B + + = + ∫ 456-/0123*30EFGH3#FGH*!8I>/';JK!LM<N -8>#+&'/FG!FHOP>'#+&'L!HKGEP!8I>>3!QR0S> FGH!EP '  )@+@(30EHLK!(>>T''#<U>S>HK! EB' 456-/0123&;20<=>-*    :    V  A :   : W x x y y x y x  + + − − =   + + − =   ∈X &'(78)-   &9:;<=!>?5@ 456&"!  )->R0S>J'#4Oxy'#<U>S>D  9  A+ =x y !D  9  Ax y− = ;J)#<U> -Y0Z!QD  /F,D  /'#+G!''>FG!8I>/G[0<=>-* &')'>FG3D2@\>   !#+F3#4D<=>  )->(I>>'J'#4Oxyz#<U>S>   9    x y z− + ∆ = = − !R0S>]9−^A ;J>'#+&'∆!Q]K#+84∆)@(>_K#]K `  456&""#)*0M&'0a^       z i i= + − A&9:;<=!>?4!;": 456&B!  )->R0S>J'#4Oxy'>FG1/F3#bA`O`#<U>S>#c8'-8>#+ &'/AB!AC30<=>-*x + y − :A)*J'#4#bB!C#+dO− \- #<U>'#c8'#bC&''>#6  )->(I>>'J'#4 Oxyz#+ AAOAO −!#<U>S>     9    x y z+ − + ∆ = = )@ (>_A#∆[0<=>-*RM81A,∆/'#+B!C'BCe 456&B-0123& 0a^5'6      i z i − = − )*I#8&'0a z iz+ AC)+ 459     )f0#%Xg  :OgA⇔A' :  O  G;Hhi) i7@)a  x y →−∞ = −∞ !  x y →+∞ = +∞  −∞ A :  ∞ g  A− A  ∞ −∞i V W − ) P#$>- −jOAO :  OjO>%- AO :   P#/#//AOAO#/+8/ :  O :   V W − k ` :x − OlA⇔   i+8C   O  W  i$%9  ]<=>-*#4>'#+&'#$%!-.9     A⇔  A ⇔'>  A ;J    >2&'0<=>-*[Q#78(2:mA'39     O    H#3 8M8<=>#<=>!Q9      : A >  A    :  + >  = − ≠  + + <   ⇔        :  A        > −   − ≠  + − <    ⇔   :  A     > −   ≠  + <    ⇔   :  A    > −   ≠  <     ⇔    :  A   − < <  ≠   45i78(29  Ax ≠ !' n 'op ])⇔          ' x x x x x x + + + = + ⇔            x x x x x x x x + + + = +            A     A      W     ` ` x x x x x x x loai hay x x k hay x k k ⇔ + + = ⇔ + = ⇔ − − = ⇔ = = − π π ⇔ = − + π = + π ∈ ¢  i78(2qA G?0<=>-*⇔         A     − − + − + ≥ − − +    A  :   V W − rKs8tA⇔     − + > ⇔  mA+  H#3?0<=>-*⇔       − − + − + uA ⇔       − + ≤ − + + ⇔     A       A  − + + ≥  − + − + ≤  ⇔     A     A  − + + ≥  − + ≤  ⇔   = − ⇔ {  A      ≤ ≤ = − ⇔ {  A      A ≤ ≤ − + = ⇔ A    V   ≤ ≤   ±  =   ⇔  V   − =  (9  i78(2≥A L1 v B w 9            A  :  x x x     − − + = − − + ≤ − <    ÷       ⇔    x x x x− ≤ − − + xA(I>' y  xmA9     x x x x   ⇔ − ≤ − + −  ÷        x x x x   ⇔ + − ≤ − +  ÷   iz v     t x x t x x = − ⇒ + = + ' n 9            x t t t t t t ≥ −  + ≤ + ⇔  + ≤ + +  x     A   A t t t t− + ≤ ⇔ − ≤ ⇔ =     A  V `  V  V  :   V    x x x x x x x loai ⇔ − = ⇔ + − =  − + =  − −  ⇔ ⇔ = =  − − =   45&      A A A        x x x x x x e e e I dx x dx dx e e + + = = + + + ∫ ∫ ∫ D      A A  O   x I x dx= = = ∫    A   x x e I dx e = + ∫ E  A        x x d e e + + ∫ E  A      x e+        e+    ÷   [1 v C         e+   +  ÷   456 E LHK       V     e a a a a a   − − =  ÷   #!D⇒[ ELHK     V V    e : a a a = #!    V :  a a NC a= + =  )'3'>!8I>FKH!LH\>'8 L  · · NCD ADM= !fHK!8I>L [f)'39     V V  a a DC HC NC HC a = ⇒ = =  )'3'>EP!8I>/P!(5'>&'HK!E@78'!"_P->'> EP L           V  {   :   { a h h HC SH a a a = + = + = ⇒ = 456i9  : x ≤ iz v 8O V v y= − ]-= y ' n 88  !!  ⇔8p!8  8!!  A⇔uv L>| } '' n 9   A :  V  V :  x x y x y  ≤ ≤   = − ⇔  −  =   ]-= y ' n   : V ` :   : W x : x x x− + + − = ~B w ' n I w  :  V   : `   : : f x x x x= − + + − -   AO :        : •  : :   : f x x x x = − − − tA Kz v (' w 9  W  f   =  ÷    x w > v D81 w    !' n  [1 v  v  w > v D81 w    !' n  &9:;<=!>?5@ 456&"  F∈D  ⇒F'O a− 'mA ]Fc8'F⊥D  9  : Ax y a− − = F∩D  −'O  a−  ]FGc8'F⊥D  9   Ax y a+ + = FG∩D  G  O   a a   − −  ÷  ÷           O  O O          O O    9        ABC S BA BC a A C Tâm I IA Pt T x y ∆     = ⇔ = ⇔ = ⇒ − − −  ÷  ÷     −       ⇒ − = = ⇒ + + + =  ÷  ÷  ÷       ¡  OO∈∆ ∈]⇒A⇒⇒OO KOO K  `⇔      `⇔`  `⇔± ⇔A' : GF H P K L E [fK  OAOOK  OOA DK  ]  A   ` ` − − = ODK  ]  : A `  ` − + + = 456&"  ^     = + −     + −  V + ⇔ ^ V = − ⇒]M&'0a^ − A&9:;<=!>?4!;": 456&B  ]<=>-*#<U>'FP9``A⇔A ;J>'#+&'C€!FP!QC€9:A8-'>2&'2 {   A   : − = + = ⇒O -8>#+&'FP⇔ { P  F P  F    : `     : `  = − = − = − = − = − = − ⇔PpOp ]<=>-*G9A⇔:A ;JGOp:∈G HP-8>#+&'G⇒p:OOdOp )'39 d V O  = + − − uuur !8I>>3!Q GF ` O A= − + uuur ⇒V`pAA ⇒  A⇒A'p` [fG  AOp:O  p:OA'G  p`OO  Op`  ∆c8'KpOOp[)] ' OO= r O FK  OO = − − uuuur ⇒ ' FK  WO OA∧ = − − r uuuur ⇒DF∆ ' FK :{ : AA V W : { : ' ∧ + + = = + + r uuuur r  ["GP!8I>>3!Q∆ )'39GP G :  = ∆FPG⇒X   V :V ` W W + = V ]<=>-*E9      ^  V+ + + = 456&B    ^   − = −           π π   − = − + −  ÷    ⇒ ( )    e    − = −π + −π  e− ⇒ e e  ^ : :    − − + = = = − − − ⇒ ^ ^ : :  : :+ = − − + − +  e − + ⇒ ^ ^ e + = $%&'($%&)* +, -.)/'$)01$234456443 )70%&)809+# V A   !"#$%(khơng kể thời gian phát đề) '()*+, 45#+Cho hàm s y =     + + # 1. Khảo sát sự biến thiên và vẽ đồ thò (C) của hàm số đã cho.  )*#+#<U>S>p,#$%/'#+012FG''>•FG3 D2@\>  •>J'#4 Câu IIAđiểm  ;0<=>-*A  ;0<=>-*    `  : e Ax x x x+ − − + − − = ∈X 45A#+)@@01C       e x dx x x+ ∫ 456A#+*z>-.'>#78FGFgGgg3FG'>3>T''R0S>FgG !FG\>`A A ;J;-J>1'>FgG)@+@(z>-.#6!@(@ RM8>/0aD2;FGB' 456A#+(I>1'5'69')*>-%5?&'+8 aK'          '  ''     a b c+ +  '(78)-F/0123 GH;I0<J;KL22M>:!"$N-$N:O;A3 &9:;<=!>?5@ 456&"A#+  )->R0S>J'#4•'>FG!8I>/F3#bp:O01>->>3F3 0<=>-*VA[0<=>-*#<U>S>GD2@'>FG\>:! #bF3#4D<=>  )->(I>>'J'#4•^#+FOAOAGAOOAAOAO->#3D<=>! R0S>]9^A~#%!R0S>FG!8I>>3!QR0S>]! (>_#+•#R0S>FG\>    456&"A#+)->R0S>J'#4•*f0N0#++8D‚0a^5'69  z i i z− = +  A&9:<=!>?4!": 456&BA#+  )->R0S>J'#4•#+FO  !B0d9      x y + = ;Jƒ  !ƒ   8#+ &'dƒ  3#41OK>'#+38>#4D<=>&'#<U>S>Fƒ  !QdOL#+ #a>&'ƒ  c8'K[0<=>-*#<U>-Y>/0'>FLƒ    )->(I>>'J'#4•^#<U>S>∆9     x y z− = = ~#%J'#4#+K- -. '(>_K#∆\>•K 456&BA#+ ;b'20<=>-*9     >    :   − =   + =  ∈X AC)+ '()*+, ` •  p   pp   − V  45& { } ( ) „   …  O A  D y x D x = − = > ∀ ∈ + ¡ )i9p!*      x x y y − + →− → = +∞ = −∞ O)L9!*   x y →±∞ = P#$>- −∞O−!−O∞P(I>3-%  pjpj g   j pj  ]<=>-*#4>'#+&'!#<U>S>p ( ) ( )      :  A x  x x m x m x m x + = − + ⇔ + − + − = + !*p(I>>2 ]<=>-*x3  e Am m∆ = + > ∀  D8I,/#+FG)'39 ( ) ( )         OAB A B B A A B B A S x y x y x x m x x m ∆ = ⇔ − = ⇔ − + − − + = ( ) ( )      A B A B m x x m x x⇔ − = ⇔ − =   e  : m m + ⇔ = :   e :e A : m m m m⇔ + − = ⇔ = ⇔ = ± 45&  A ⇔  A ⇔A ⇔A⇔A ⇔  k π π + ⇔ :  k π π + (∈†     `  : e Ax x x x+ − − + − − = #78(29   `  − ≤ ≤ ⇔    :  `  : V Ax x x x+ − + − − + − − = ⇔  V V  V  A   :  ` x x x x x x − − + + − + = + + + − ⇔VA'     A   :  ` x x x + + + = + + + − !I>2⇔V 45& W ( )      e x I dx x x = + ∫ O  u x du dx x = ⇒ =  B 8 A ( ) ( )     A A      u I du du u u u   = = −  ÷  ÷ + + +   ∫ ∫   A     u u   = + +  ÷ +   ( )         = + − +  ÷           = −  ÷   456& ;JP-8>#+&'GB>8'39 · A F•PF `A= )'39FP '   FgPFP '  !FFg '     '  [f+@(z>-.[  '  ' :    '  e ‡#<U>-8>-&';F/-8>#+K&';F ->R0S>FgFP,;C/€*;€(@ RM8>/0aD2;FG )'39;K;F;€;C ⇒X;€ GM GA GI       GA GI IA GI GI + =  W  a 456&iR'''39'      q'' ⇒'  '      ''q'' ⇒'      !  A  t≤ ≤ )BGE'39  ''  u'          '   ⇒Kq       t t t f t+ + − = ˆg      t t + − −  ˆgg      t − − tA∀∈  A        ⇒ˆg>   •  •      f t f≥ = − mA⇒ˆz>⇒ˆqˆA∀∈  A        ⇒Kq∀'(I>15'' 'A!*K[fK '(78) &9:;<=!>?5@ 456&"&  [*p:O µ F !8I>!01>-> >3FD9VA F mA F:O ⇒Fe KD2@∆FG: FG` KR(FG!8I>>3!Q-.  G:OW [f0<=>-*&'G9:`A  FOAOAOGAOOAOAOAO!QmA e F G  D Fg F G  g Gg P ; C K ⇒FG9   x y z b c + + = ⇒FG9^A [*  D  AO  FG                bc b c b c = + +  ⇒                      ⇔         ]9^A3[)]) AOO  P n = − uur FG3[)])  O O n bc c b= r [*]!8I>>3!QFG⇒  A P P n n n n⊥ ⇔ = r uur r uur ⇒A )_!mA8-'9 456&"& ^'E8-'9  z i a b i− = + − !^'''  z i i z− = + ⇔          a b a b a b+ − = − + + ⇔'    '    ⇔'    A⇔'     [f^'!Q'5''     A&9:<=!>?4!": 456&B&  ( )      9       x y E c a b+ = ⇒ = − = − = H#3ƒ  pOAOƒ  OAOFƒ  30<=>-*   Ax y− + = ⇒K  O     ÷   ⇒L : O     ÷   ⇒  LF O    = −  ÷   uuur O ( )  ƒ F O = uuur ⇒  LFƒ F A= uuur uuur ⇒∆FLƒ  !8I>/F #<U>-Y>/0'>3#<U>(@ƒ  LH#3#<U>-Y 30<=>-*9    :     x y   − + − =  ÷    DKO∆ LK' ' ∆ ∆ uuuur uur uur K∈•⇔KOAOA ∆c8'LAOOA3[)] ' r OO LK O OA= − uuuur ⇒ ' LK OO     = − −   r uuuur )'39DK∆•K⇔ ' LK •K '     = r uuuur r ⇔  V : e   + + = ⇔:  :eA⇔−'[fK−OAOA'KOAOA 456&B&     >    :   − =   + =  ⇔        :    − =   + =   ⇔         :    + =    + =  ⇔          :      + =    + = +  ⇔        :   A  + =    + − =  ⇔            A   + =     + − =   ⇔           + =     =   ⇔      = −    =   iR>L>J‰ iR>L>JPŠ> )-8>1GH[P!‰)iPpEi)9A{WW:`WW{ )P])pL>JP$p)8 { /P)  Q R Q S  !"#$%(không kể thời gian phát đề) 'T U )T Q  V  Q -./0W V 23 45-/0W V 23' n I w  :  `y x x= − − + ' y ' w < v  w  !' n !B } #I n  v 8 y '' n I w #' }  [ w 0<=>-| n  w 08 w 8 y '#I n  v  w  w 08 w !8I>> w != w #<= n >z y >   ` y x= − 45-/0W V 23 ;' y 0<=>-| n         Ax x x x− + − − = ;' y 0<=>-| n        : : :  :    x x x x x x x + + + + + − + = + ∈ ¡ 45-/0W V 23)| w | w 01     e I x xdx x   = −  ÷   ∫ 456-/0W V 23| n  w 0S.ABCD w #' w ABCD' n | n !8I>' v a' v  SA = aO| n   w 8!8I>> w 8 y '#| y S- z v 0z y >(ABCD)' n # y H8I v #' v AC, : AC AH = . ; v CM ' n #<= n >'8 y ''>' w SAC< w >M' n -8># y 8 y 'SA!' n | w  y | w (I w < w D v SMBC Ba 456-/0W V 23)| n >' w - v  y 1 w 8 y '' n I w    :   Ay x x x x= − + + − − + + 'T U 78)-F/0W V 23 : ; : < = >  ? @ > ,?-$4 U :X Y ;A3 &9:;<=!>Z U 54 V  456&"-/0W V 23  )->z v 0z y >' v #I v •'>' w FG w #| y FOpW-< v 1' n POp1#<= n >- n  >' v  w 0' n CpOA~' w # v ' v #I v #| y  w  w ' n #I v D<=>  )->(I>>'' v #I v •^'z v 0z y >]9^−A!' n ‹9−^−A[ w  0<=>-| n z v 0z y >X!8I>> w != w ]!' n ‹'(' y >' w < n •# w Xz n > 456&"-/0W V 23)| n I w 0< w ^' y ' }  z = !' n ^  ' n I w 81 n ' y  A&9:;<=!>Z U 4!;": 456&B-/0W V 23  )->z v 0z y >' v #I v •# y FAO!' n ∆' n #<= n >z y >#c8'•; v P' n | n  w 8 !8I>> w 8 y 'F- ∆[ w 0<=>-| n #<= n >z y >∆ w (' y >' w < n P# w -8 v ' n z n > FP  )->(I>>'' v #I v •^'#<= n >z y >∆  9 x t y t z t = +   =   =  !' n ∆  9      x y z− − = = ~' w # v  ' v #I v # y K8I v ∆  '(' y >' w < n K# w ∆  z n > 456&B-/0W V 23;' y  v 0<=>-| n     :  A    >   > A x x y x y x y  − + + =  ∈  − − =   ¡ A U ) V )[ Y  Q 'T U )T Q  V  Q -./0W V 23 45 :  `  y x x C= − − + „' y ' w !B }  )~i9HXO    • :  O • A    A AO `y x x y x x x y= − − = ⇔ − + = ⇒ = = A [...]... SĐT:0977467739 THPT Ngọc Hồi- KonTum.) Nếu thật sự không muốn mình là người thừa xã hội./ Bến bờ thành công là không có dấu chân của kẻ lười biếng./ Em cắm hoa tươi đặt cạnh bàn, Mong rằng Toán học bớt khô khan Em ơi trong Toán nhiều công thức, Vẫn đẹp như hoa lại chẳng tàn (Kỉ niệm)  18 ... = 0  x = 4   ⇒ x = 3; y = 1 x = 4; y = − 2 Đặng Ngọc Liên, Đặng Ngọc Hùng (Trung tâm BDVH và LTĐH- SĐT:0977467739 THPT Ngọc Hồi- KonTum.) ÐỀ THI TUYỂN SINH CAO ĐẲNG KHỐI A, B, D NĂM 2010 Môn thi : TOÁN Thời gian: 180 phút (không kể thời gian phát đề) I PHẦN CHUNG CHO TẤT CẢ THÍ SINH (7,0 điểm) Câu I (2,0 điểm) 1 Khảo sát sự biến thiên và vẽ đồ thị (C) của hàm số y= x3 + 3x2 – 1 2 Viết phương trình... Trong không gian với hệ tọa độ Oxyz, cho hai điểm A (1; -2; 3), B (-1; 0; 1) và mặt phẳng (P): x + y + z + 4 = 0 1 Tìm tọa độ hình chiếu vuông góc của A trên (P) AB 2 Viết phương trình mặt cầu (S) có bán kính bằng , có tâm thuộc đường thẳng AB và (S) tiếp xúc với 6 (P) Câu VII.a (1,0 điểm) Cho số phức z thỏa mãn điều kiện (2 – 3i)z + (4+i) z = -(1+3i)2 Tìm phần thực và phần ảo của z B Theo chương trình... (∆) ∩ (P) nên tọa độ H thỏa :  x = −1 x + y + z + 4 = 0    x − 1 y + 2 z − 3 ⇔  y = −4 Vậy H (-1; -4; 1)  1 = 1 = 1 z = 1   uu ur 2 Ta có AB = 4 + 4 + 4 = 12 = 2 3 và AB = (-2; 2; -2) AB 1 = Bán kính mặt cầu (S) là R = 6 3 x +1 y z −1 = = (AB) : Vì tâm I ∈ (AB) ⇒ I (t – 1; – t; t + 1) 1 −1 1 (S) tiếp xúc (P) nên d (I; (P)) = R ⇔ t + 4 = 1 ⇔ t = -3 hay t = -5 ⇒ I (-4; 3; -2) hay I (-6; 5; -4)... = 1 3  10 x − 15 = −7 x + 14 ⇔ 17 x = 29 ⇔     x = 29 (loai )   17   12 x y' y −2 − 1/3 0 + y(1/3) 5 1 y  ÷ = 2; ymin = 2  3 Cách khác: có thể không cần bảng biến thiên, chỉ cần so sánh y(-2), y(1/3) và y(5) PHẦN RIÊNG (3,0 điể m) Thí sinh chỉ được làm một trong hai phầ n (phầ n A hoă ̣c B) A Theo chương trinh Chuẩ n ̀ Câu VI.a: 1/ * C1: Nố i dài AH cắ t đường tròn