Bộ đề thi thử đại học môn toán có đáp án năm 2014

  Thời gian làm bài : 180 phút  ! "#$ !   − + = x x y     !"#$%&'(%)*+,+* "#$$ ! -./0$&"1 + + 23 4 32 =       −+       + ππ xx -5./0$&"1 + 2 3   ≥ − −− xx xx "# !".6$7$89:/;$1 <+< +−=== xyxyx !=%=>&?@A9>"7B(AB(&CDA "#% ! EF$&C$'(),)  ,     9AG$*9G$ a =% =>EF$&C$H$#)  /;$)7.), "#% !1 42  =++ cba !"$&E85I51        ∈++=   *+ π xxcxbay &'( ! Thí sinh chỉ được làm một trong hai phần (phần 1 hoặc phần 2 )*+,) /0123/),)#4/ "#%5$ ! !&$J.6$8KLMD@A/;$&?1 +N  =−−−+ yxyx /;$6$O1 + =++ yx !"#$%P(M/;$6$OQ %P>R/S .(AS.8($HT+ + !&$>U$$8KLMD@AVJW(X1 ( ) ( ) T    =+++− zyx  YZ../0$&"J.6$[(U$$H8/;$6$1    − = − = zyx \ JW(X] /;$&?H>=G$ "#%5 ! H($#>(^'(E80++ $)*+,) /0123/)/"/0,5+ "#%6$ ! !&$J.6$8KLMD@A]E._1 +NN  =−+ yx !"#$%` &]E._ 1 +  4+ a =FNF b  *b  E(%]E._ !&$U$$8KLMD@AV/;$6$      = = = ∆  1 z ty tx % *+* −A 777+5/5895*1  !"LM%_b(M/;$6$ ∆ %$)_bE$'( "#%6 ! !".cVI 1      =− +−=− N   zz izziz    d( e. e% $  ! $:! f!Z.@1g R= h         fX1 Dx x y ∈∀< − − = +  2  f i7f$& *   <   * ∞+−∞ <7f>U$H& i-89jKZ1  ∞−=∞+=== −+ →→ −∞→+∞→ yLimyLimyLimyLim xx xx     <<   !KZ$$Ak   <!KZc$@k   fe1e@k+*Akl Ak+*@kleZ$%KZEd@c$ +*2 +*2 +*2 +*2 777+5/5895*1    l ∞+ ∞−   ll ∞+ m f @    A @    l ∞+ ∞−   ll ∞+ m f m f f f fff @   A @ +*2 $ ! [/;$&($&L),1Ak@ `#$%(M'(),H$ME$K.1 x x x = − +      2   +  2  x x x x  − =   ↔ − − = ↔  + =   7%&IA1         ++         −−  2 *  2 <  2 *  2 +*2 +*2 $  !  ! [ 2 3 3 2 + 2 3 32   x x x x π π     ↔ + + − = ↔ =  ÷  ÷       3 3 2 3   3 N N 3 +x x x x x x↔ = − ↔ + − =    + 3     + x x x =  ↔  − − =     3  &   Zk kx kx ∈      +−±= = ↔ π π +*2 +*2 +*2 +*2 $ ! ,.        3  + 2 2 + + <      3  +   2 + 2 +  x x x x x x x x x x x x x x x x   = − ∨ =      − − =        ≠ ∧ ≠   ≠ ≠      ↔ ↔      <− ∨ > − − >         − >      < ∨ >             > = −≤ ↔  2    x x x  +*2   ! [/0$&"($M$%1   N   +N2 +   =↔         = = ≤ ↔    =+− ≥− ↔−= y ly y y yy y yy +*2 777+5/5895*1 3 e/;$6$Akj@\&C($9Ak !%=>&?@AW"1nkn  in  !&$Hn  k      + y dyy ππ = ∫  + k  π  n   ∫ ∫ − =−−=−=       3  3   y ydydyy πππ k 3 π  nk  4 2 đvtt π +*2 +*2 +*2 %  ! %  ! i!%=EF$&C1n N 4  3  aAAABCdt == i)7*)  k       ACAH CAAAAH ACAH ACAH       + = →→→ →→ k     ACAH CAAH →→  +   + 4+*   3  3  3   3  3+ =→=== ACAH aa aa ACAH ACAH nZA)7*)   k4+ +  nZA)7*)  k4+ +   ( )( ) ( ) xxxxcbay 42  ++=++++≤ eJo@k N  xxxxx −++=++ o@k 4N N ++− xx *eJ ( ) *+*  ∈= ttx $k N 3 +<4p4N ff =↔=+−=→++− ttgttgtt ,,! P       P@$ 3N 3  N 3 N 3  π =→=↔== xxtkhi    2 3  2 3 N 3 42  ≤≤−→≤ yy O5(qkr@A&> 3 π =x  c x b x a  ==  A cba  3  4 ==  +*2 +*2 +*2 +*2 + +*2 +*2 777+5/5895*1 N  o oo +  N 3 + i l N 3    o o o +  N 3 + i l N 3   !A1        −= −= −= ∨        = = = →=++ 2 3+ 2 2 3+ 2 42  c b a c b a cba  %5$ !   iHds*>=tk 4  i BABMA *T+ a + = E.%(A&1  === RMAMI nZAP(M/;$&?ds>=t f k  P(MOP@*AH LMIK1  ( ) ( )      +−= −= ∨      −−= = ↔      =++ =−+−     +   y x y x yx yx nZAH%IA(W(HLM(& *+% XHd *+* −J >=tk3 iH. ** − → u *[(U$$H8[Z → u E. [.[HO9$1 + =+−+ Dzyx i[\X]/;$&?H>&kOu*[k 2  =− rR H1 2 3 + = +−−+ D      −−= +−= ↔ 232 232 D D Y1HJ.6$1[  1 +232 =+−−+ zyx [  1 +232 =−−−+ zyx +*2 +*2 +*2 +*2 +*2 %5  ! %5 $   -LW"HO9$1 abcd i`(v1HwL 3 T A L**O i`(k1 iv+1HpLH  p A L*O ik+v1HwLwLO ik+k1HwLO nZAIA(W(E1 N+3wwwpw  p 3 T =+++ AA  ! _1 33<<N< N   =→=−==→==→==+ cbacbbaay x ix.OC$E=U&$$b  `b  1  p  < T 3 3 N  3 N   4+         +        ==↔ =−=↔ −−+=↔ −+= yx caNFNF NFNFNFNFNFNFFF NFNFNFNFFF nZAHN%IA(W(1 +*2 +*2 +*2 +*2 +*2 +*2 +*2 777+5/5895*1 2         −−         −         −         3  * 3 N < 3  * 3 N < 3  * 3 N < 3  * 3 N N3 NNNN +*2 $ ! ie/;$6$ *+*+ + Mquađi∆ H. +** → u < **N*<*+* ++ −=       −= →→→ uAMAM i$Q) ∆ E)7k 2 4 * * + =       =∆ → →→ u uAM Ad i!$)_b'( 2 N 3   ===→ AHAFAE nZA_*b(MJW(d)* ,tk 2 N /;$6$ ∆ *LM_*bE$KK1          =+++− = = = 2 3     zyx z ty tx +*2 +*2 +*2 k 2   (A&LM_bE1            = + = + = ∨            = − = − =  2 N 2   2 N 2  z y x z y x +*2 %6   ! i-L.cVk@iA * Ryx ∈ 7K      = +=−+ ↔ NN  xyi iyiyx       = = ↔        −=∨= = ↔ 3 3  N  N  N y x x y x y x y nZA.cW"E1 iz 3 3 N  N += +*2 +*2+ +*2 $  "#      x y x − = − 777+5/5895*1 4 o  o f   n./0$&".(A*>$Q%s<.(A G$   "#  -./0$&"  w   4  3  +      x x x x π π + + = + +  -K./0$&"1 N 3   3    x x y x y x y x xy  − + =   − + = −   "#;!==.d1sk N +  E   x x dx x π ∫ "#%; "H.X),HA),E$(U$9)8),k*JE $d9yX7J.6$X),X)z$98J.6$A$H4+ +  !=U$H$#J.6$X),X, "#%;**EO/0$I iikc$&G$1  3 a b b c c a ab c bc a ca b + + + + + ≥ + + + &'  !"# < )*+,) /0123/))#4/ "#%5 !&$J.6$LMD@A%)</;$6$ ∆ 1@i3AiNk+ !"LM%,(M/;$6$ ∆ /;$6$), ∆ S.8($H N2 +  !&$>U$$8KLMD@AV*%P<l< /;$6$    1   3 x y z d + = = − −   N  { 1   2 x y z d − − = = c$1%P*O*O|z$G&MJ.6$n./0$&"J.6$ H "#%5 -./0$&"1    N  N  N  E$ E$ x x x x x Log x x x + + + + =  )*+,) /0123/)"/0,5+ "#%6 !&$J.6$LMD@A/;$&?    1 C x y+ = */;$6$   1 +d x y m+ + = !" m %  C \  d 9),OK=$),DE8 5 !&$>U$$8KLMD@AV*J.6$1 [1@jAiVik+*}1@jAiVi3k+*t1@iAj3Vik+ /;$6$  ∆ 1   − −x k  +y k 3 z -L  ∆ E$(A[} n./0$&"/;$6$O(U$$H8t\/;$6$  ∆ *  ∆  "#%6 -5./0$&"1E$ @ E$ 3 T @ jw ≤  777+5/5895*1 w $ "#=> ?@#/0   ~!Z.@1 { } h D = ¡ ~!=   { +   y x D x − = < ∀ ∈ − 7$&>$  <−∞  < +∞ ~7>U$H& ~-89  + → = +∞ x lim y  x Limy − → = −∞  x Lim y →+∞ =   x Lim y →−∞ = eHKZc$1@k*KZ$$Ak ~,$ @ −∞  +∞ A| ll A  +∞  −∞   ~n +2 +2 +2 +2  ~!.(A9% + +  <    M x f x C∈ H./0$&"  + + + {    y f x x x f x= − + 7A   + + +      +x x y x x+ − − + − = ~ ~$Q%s<.(A~G$   + N +       x x − ⇔ = + −  $/S$K + +x =  + x = ~.(AW"1  +x y+ − =  2 +x y+ − = +2 +2 +2 +2  ~,•./0$&" /0$/0$8   3   +   4 + 4 c x x c x π − + + + =    2   3 + 3 4 c x c x π π ⇔ + + + + =       2    + 4 4 c x c x π π ⇔ + + + + = -/S    4  c x π + = −     4 c x π + = − E9 +2 +2 777+5/5895*1 p ~-    4  c x π + = − /S$K   x k π π = +  2  4 x k π π = − + +2 +2  ~,•K/0$/0$8   3 3        x xy x y x y x xy  − = −   − − = −   ~eJ€.C  3 x xy u x y v  − =   =   */SK    u v v u  = −  − = −  ~-K&/S$K(<E<+l<l3 ~!QH$/S$K@<AE<+l<+ +2 +2 +2 +2 3 ~eJk@ !=Okl@O@*•Z@k+"k* N x π = "   t = !QH         E Et t I dt dt t t = − = ∫ ∫ ~eJ   E <u t dv dt t = =    <du dt v t t ⇒ = = − X(A&           E E       I t dt t t t = − + = − − ∫ ~B(    E   I = − −  +2 +2 +2 +2 N ~n" ~-L7E&($%,*c$  SH ABC⊥ ~•‚$$H$#J.6$X),*X)8JAE  + 4+SEH SFH= = ~R HK SB⊥ *EZ.E(Z(A&$H$#J.6$X),X, G$ HKA  ~YZ.E(Z=/S)k),k*   a HA = * + 3  4+  a SH HF= = ~!$X7(U$97H       3 + KH a HK HS HB = + ⇒ = ~!$)7(U$97H  +   3 3 + a AH AK H KH a = = = +2 +2 +2 777+5/5895*1 T  3  3 AK H⇒ =  +2 2 ~,•       a b c c ab c ab b a a b + − − = = + + − − − − ~!QH             c b a VT a b c a c b − − − = + + − − − − − − g**O/0$iik**(M>$+<kvl*l*l O/0$ ~.OC$56$cUO/0$/S 3    3            c b a VT a b c a c b − − − ≥ − − − − − − k3. e6$c@A&>y>  3 a b c= = = +2 +2 +2 +2 4 ~ ∆ H./0$&"  3   x t y t = −   = − +  H.  3<u = − ur ~)(M ∆   3 <   A t t⇒ − − +  ~!H),< ∆ kN2 +    <   c AB u⇔ = uuuur ur      AB u AB u ⇔ = uuuur ur ur   2 3 4T 24 N2 + 3 3 t t t t⇔ − − = ⇔ = ∨ = − ~%W"E   3 N  3  < *  <  3 3 3 3 A A− − +2 +2 +2 +2 4 ~OB(  +< <+M − H.  < < 3u = − − uur O|B(  +<<NM H.  <<2u = uur ~!H   <  N< p<Nu u O   = − − ≠   uur uur ur *   +<<NM M = uuuuuuur •ƒ     <  4 N +u u M M   = − + =   uur uur uuuuuuur OO|$.6$ ~-L[EJ.6$cOO|kv[H. << n = − ur B( P  H./0$&"   +x y z+ − + = ~g„5A%P<l<(Mo[*QHH. +2 +2 +2 +2 w ~e'(>K1@v+ ~!71@ƒ@kE$K ~!71@ƒ x ≠ *•./0$&"/0$/0$8      E$ N   E$ N  E$ N  x x x x x x + = + + + + + eJ E$   x x t+ = */S./0$&"       t t t + = + + $/Skklf3 ~n8k E$    x x⇒ + = ./0$&"AU$K +2 +2 +2 777+5/5895*1 + [...]... + + Cn = = 2 3 n +1 2(n + 1) n + 1 2(n + 1) 3 3n +1 = 243 n = 4 Vy n=4 05 05 05 THI TUYN SINH I HC 7 Môn: TOáN (Thời gian làm bài: 180 phút) Phần chung cho tất cả thí sinh (7,0 điểm) Câu I (2 điểm) Cho hàm số y = 2x +1 x +1 1 Khảo sát sự biến thi n và vẽ đồ thị (C) của hàm số đã cho 2 Tìm trên (C) những điểm có tổng khoảng cách đến hai tiệm cận của (C) nhỏ nhất Câu II (2 điểm) x+1 + y 1 = 4 1... có 7.6.5.4.3 = 2520số Nếu b = 7 thì có 6 cách chọn a, 6 cách chọn c, 5 cách chọn d, 4 cách chọn e, 3 cách chọn f ở đây có 6.6.5.4.3 = 2160số Tơng tự với c, d, e, f Vậy tất cả có 2520+5.2160 = 13320 số VIII a Tìm a để (1,0 điểm) Điều kiện: ax + a > 0 Bpt tơng đơng x 2 + 1 < a( x + 1) Nếu a>0 thì x +1 >0.Ta có 0,5 0,25 0,25 0,5 0,25 x2 + 1 0 và a2+b2-ab ab a3 + b3+1 (a+b)ab+abc=ab(a+b+c)>0 0,5 1 1 3 3 a + b + 1 ab ( a + b + c ) Tơng tự ta có 1 1 , 3 b + c + 1 bc ( a + b + c ) 1 1 3 c + a + 1 ca ( a + b + c ) 3 3 Cộng theo vế ta có 1 1 1 1 1 1 + + = 3 + 3 3 + 3 3 3 x + y +1 y + z +1 z... (1,0 điểm) 5 5 Ta có: AB = 2 , M = ( ; ), pt AB: x y 5 = 0 2 2 3 1 3 S ABC = d(C, AB).AB = d(C, AB)= 2 2 2 Gọi G(t;3t-8) là trọng tâm tam giác ABC thì d(G, AB)= d(G, AB)= t (3t 8) 5 = 0,25 1 2 1 t = 1 hoặc t = 2 2 2 G(1; - 5) hoặc G(2; - 2) u ur u ur uu uu Mà CM = 3GM C = (-2; 10) hoặc C = (1; -4) VII a Từ các chữ số (1,0 điểm) Gọi số có 6 chữ số là abcdef Nếu a = 7 thì có 7 cách chọn b, . !!=%=>&?@A9>B(AB(&C".6$/S $89:/;$1AkE@<Ak+<@k Thí sinh không được dùng tài liệu, cán bộ coi thi không giải thích gì thêm! llllllllll7llllllllll NO "# ?@#/0 $ . = +2 +2 +2 +2  ( AB/; (Thời gian làm bài 180 phút, không kể thời gian phát đề) ! "#( 2,0 điểm):  N   x y x − = +   $!"&%@c$(B(/;$6$P`Pl3<+`l<l "#(2,0