DE - DAP AN DE DH KHOI A MON TOAN 2010

ÐỀ THI TUYỂN SINH ĐẠI HỌC KHỐI A NĂM 2010 Môn thi : TOÁN I. PHẦN CHUNG CHO TẤT CẢ THÍ SINH (7,0 điểm) Câu I(2,0 điểm)       !!"#$%&'(  )*#+#$%&', /#+0123 #4      5'6#78(29          :+ + < Câu II (2,0 điểm)  ;0<=>-*       :    '   π   + + +  ÷   = +  ;?0<=>-*9         − ≥ − − + Câu III (1,0 điểm) )@@019       A  B  B C D  B + + = + ∫ Câu IV (1,0 điểm)*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' Câu V (1,0 điểm).;20<=>-*    :    V  A :   : W x x y y x y x  + + − − =   + + − =   ∈X II. PHẦN RIÊNG (3,0 điểm) Thí sinh chỉ được làm một trong hai phần (phần A hoặc B) A. Theo chương trình Chuẩn Câu VI.a (2,0 điểm)  )-> 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 `  Câu VII.a (1,0 điểm). )*0M&'0a^       z i i= + − B. Theo chương trình Nâng cao Câu VI.b (2,0 điểm)  )->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 Câu VII.b (1 điểm). 0a^5'6      i z i − = − )*I#8&'0a z iz+ GfC;CgC Câu I:9     )h0#%Xi  :OiA⇔A' :  O  x y →−∞ = −∞ !  x y →+∞ = +∞  −∞ A :  ∞ i  A− A  ∞ −∞j V W − ) P#$>- −kOAO :  OkO>%- AO :   P#/#//AOAO#/+8/ :  O :   V W − l ` :x − OmA⇔   j+8C   O  W  j$%9  ]<=>-*#4>'#+&'#$%! 9     A⇔  A ⇔'>  A ;J    >2&'0<=>-*[Q#78(2:nA'39     O    H#3 8M8<=>#<=>!Q9      : A >  A    :  + >  = − ≠  + + <   ⇔        :  A        > −   − ≠  + − <    ⇔   :  A     > −   ≠  + <    ⇔   :  A    > −   ≠  <     ⇔    :  A   − < <  ≠   Câu II: j78(29  Ax ≠ !'op ])⇔         ' x x x x x x + + + = +   A  :   V W − ⇔           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 ∈¢  j78(2qA G?0<=>-*⇔         A     − − + − + ≥ − − + rKs8tA⇔     − + > ⇔  nA+  H#3?0<=>-*⇔       − − + − + uA ⇔       − + ≤ − + + ⇔     A       A  − + + ≥  − + − + ≤  ⇔     A     A  − + + ≥  − + ≤  ⇔   = − ⇔ {  A      ≤ ≤ = − ⇔ {  A      A ≤ ≤ − + = ⇔ A    V   ≤ ≤   ±  =   ⇔  V   − =  (9  j78(2≥A Lhv9            A  :  x x x     − − + = − − + ≤ − <    ÷       ⇔    x x x x− ≤ − − + wA(I> wnA9     x x x x   ⇔ − ≤ − + −  ÷        x x x x   ⇔ + − ≤ − +  ÷   jR    t x x t x x = − ⇒ + = + 9            w t t t t t t ≥ −  + ≤ + ⇔  + ≤ + +  w     A   A t t t t− + ≤ ⇔ − ≤ ⇔ =     A  V `  V  V  :   V    x x x x x x x loai ⇔ − = ⇔ + − =  − + =  − −  ⇔ ⇔ = =  − − =   Câu III.      A A A        x x x x x x e e e I dx x dx dx e e + + = = + + + ∫ ∫ ∫ ;      A A  O   x I x dx= = = ∫   A   x x e I dx e = + ∫ =  A        x x d e e + + ∫ =  A      x e+        e+    ÷   [hC         e+   +  ÷   Câu IV: 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= !hHK!8I>L [h)'39     V V  a a DC HC NC HC a = ⇒ = =  )'3'>EP!8I>/P!(5'>&'HK!E@78' !"_P->'>EP L           V  x   :   x a h h HC SH a a a = + = + = ⇒ = Câu V : j9  : x ≤ jR8O V v y= − ]-y88  !!  ⇔8p!8  8!!  A⇔uv L>z'9   A :  V  V :  x x y x y  ≤ ≤   = − ⇔  −  =   ]-y  : V ` :   : W w : x x x− + + − = {v :  V   : `   : : f x x x x= − + + − -   AO :        : |  : :   : f x x x x = − − − tA GF H P K L E KR(9  W  f   =  ÷    w3>2D8?   ! [h23>2D8?   ! A. Theo chương trình Chuẩn Câu VI.a:  F∈D  ⇒F'O a− 'nA ]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' [hK  OAOOK  OOA DK  ]  A   ` ` − − = ODK  ]  : A `  ` − + + = Câu VII.a:  ^     = + −     + −  V + ⇔ ^ V = − ⇒]M&'0a^ − B. Theo chương trình Nâng cao Câu VI.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` [h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 :x : AA V W : x : ' ∧ + + = = + + r uuuur r  ["GP!8I>>3!Q∆ )'39GP G :  = ∆FPG⇒X   V :V ` W W + = V ]<=>-*E9      ^  V+ + + = Câu VII.b:    ^   − = −           π π   − = − + −  ÷    ⇒ ( )    e    − = −π + −π  e − ⇒ e e  ^ : :    − − + = = = − − − ⇒ ^ ^ : :  : :+ = − − + − +  e − + ⇒ ^ ^ e + = )-M[~)P>PT8[ )-8>1GH[P!•)jP[z[€ .    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. w3>2D8?   ! [h23>2D8?   ! A. Theo chương trình Chuẩn Câu VI .a:  F∈D  ⇒F'O a 'nA ]Fc8'F⊥D  9  : Ax y a − = F∩D  −'O  a  ]FGc8'F⊥D  9   Ax. )- >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  )- >