BỘ ĐỀ THI THỬ ĐẠI HỌC MÔN TOÁN CÓ LỜI GIẢI

   Thời gian làm bài : 180 phút  !"#$%&'() *+!,#$%&'()   − + = x x y   !"!##$%&'()  *+!,!-./"!%&0(.12#2 *+,!,#$%&'() 3456!-/+!7   8 9 8 =       −+       + ππ xx 3:456!-/+!7  8    ≥ − −− xx xx *+!#$%&'()+!4;!-<-=!>5?!-7 @@ +−=== xyxyx *A!.AB/C!D(E!B+!<F0(EF0(!/GHE *+-!#$%&'() IJ!-/G(-011       !EK!-(2!"!K!- a A!. ABIJ!-/G#-L-,(1  #5?!-(1<'(41 *+-!#$%&'()7 98  =++ cba *+-/&I=!!:#!M!:'(7        ∈++=   2!! π xxcxbay ./!0#$%&'() Thí sinh chỉ được làm một trong hai phần (phần 1 hoặc phần 2 12134567121+8 *+-!,#$%&'() */!-N4;!-#=O(HDE5?!-/C!7 P  =−−−+ yxyx #5?!-;!-Q7  =++ yx *+!,!-.R05?!-;!-Q(S .RBT5U  !( 40E !U4#=!(0-LV  */!-BW!--(!#=O(HDEXNY0Z7 ( ) ( ) V    =+++− zyx  [\4456!-/+!N4;!-]#0W!--L#=5?!-;!-(7    − = − = zyx #^ NY0Z_ 5?!-/C!L!BA!K!- *+-!#$%&'() L(!"0!"!-%!,B!(0`0I=!6! ,121345671*52 *+-9!,#$%&'() */!-N4;!-#=O(HDE_I4a7 PP  =−+ yx *+!,!-.b /"!_I4a (7   9 c =FNF d  2d  I("0.'(_I4a    */!-W!--(!#=O(HDEX5?!-;!-      = = = ∆  7 z ty tx #. 22 −A *+(.a#d05?!-;!- ∆ .(-1adI(-0 *+-9!#$%&'() *+4eXM()!7      =− +−=− P   zz izziz    f0 4! . !,#$ %&'() !#,:) (g*\4D&!7h R= i         gZ !"!7 Dx x y ∈∀< − − =   8  g j<g!-& !/"! 2   @   2 ∞+−∞ @<gBW!-L/& j3=!kO\!7  ∞−=∞+=== −+ →→ −∞→+∞→ yLimyLimyLimyLim xx xx     @@   *O\!!-(!-El   @*O\!e!-Dl   g%&7Dl2El El2Dl%&!\!-(.O\!IfDe!- 28 28 28 28      ∞+ ∞−    ∞+ m g D    E D     ∞+ ∞−    ∞+ m g m g g g ggg D   E D  28 ,!#$%&'() ]5?!-/0!-/(!17ElD b,!-.0%&01#L!-I!-O'(47 x x x = − +      8     8  x x x x  − =   ↔ − − = ↔  + =   <(./"!%&M(E7         ++         −−  8 2  8 @  8 2  8 28 28 !,#$ %&'() !#$%&'() ] 8   8  8!  !8   x x x x π π     ↔ + + − = ↔ =  ÷  ÷       ! !8 !   !  P P!  x x x x x x↔ = − ↔ + − =   !        x x x =  ↔  − − =       (/   Zk kx kx ∈      +−±= = ↔ π π 28 28 28 28 ,!#$%&'() 4           8 8   @           8  8   x x x x x x x x x x x x x x x x   = − ∨ =      − − =        ≠ ∧ ≠   ≠ ≠      ↔ ↔      <− ∨ > − − >         − >      < ∨ >             > = −≤ ↔  8    x x x  28 !#$ %&'() ]56!-/+!&!0!--(.7      P   P8    =↔         = = ≤ ↔    =+− ≥− ↔−= y ly y y yy y yy 5?!-;!-ElkD^/G0!-El *.AB/C!D(EY!+7nln  jn  */!-Ln  l       y dyy ππ = ∫   l  π # n   ∫ ∫ − =−−=−=            y ydydyy πππ l  π # nl  9 8 đvtt π 28 28 28 28 -!#$ &'() -!#$ %&'() j*.AIJ!-/G7n P 9    aAAABCdt == j1<21  l       ACAH CAAAAH ACAH ACAH       + = →→→ →→ l     ACAH CAAH →→      92             =→=== ACAH aa aa ACAH ACAH n\E1<21   l9   n\E1<21  l9    ( )( ) ( ) xxxxcbay !!98!!  ++=++++≤ NoDl !!P!!!  xxxxx −++=++ oDl !9!P P ++− xx 2N ( ) 22!  ∈= ttx -l P  @9p9P gg =↔=+−=→++− ttgttgtt * R       R(D- P  ! P  P   π =→=↔== xxtkhi  28 28 28 28  28 28  P  o oo   P   j  P     o o o   P   j  P       8   8  P  98  ≤≤−→≤ yy Q:0qlrDE/(B  π =x # c x b x a !! ==  (E cba    9 ==  *(E#7        −= −= −= ∨        = = = →=++ 8  8 8  8 98  c b a c b a cba  -!,#$%&'() !#$%&'( jLfs2#!BA!tl 9  j BABMA 2V c  = I 4.0E/(7  === RMAMI n\ER05?!-/C!fs!BA!t g l  #R0Q!"!RD2EL (M(O7  ( ) ( )      +−= −= ∨      −−= = ↔      =++ =−+−        y x y x yx yx n\EL.M(E"0Y0!L(!"0/"! 2. (ZLf 22 −J !BA!tl j(L#4 22 − → u 2]#0W!--L#=(!"!]!\! → u I#4 ]4]LQ!-7  =+−+ Dzyx j]^Z_5?!-/C!LB/l!"!Qu2]l 8  =− rR !"!(L7 8   = +−−+ D      −−= +−= ↔ 88 88 D D [7LN4;!-7]  7 88 =+−−+ zyx #]  7 88 =−−−+ zyx 28 28 28 28 28 -!#$ %&'() - !,#$ 3Y!+LQ!-7 abcd jb 0(v7Lw!(#  V A !22Q jb 0(l7 jv7Lp!#L  p A !2Q jl#v7Lw!##w!Q jl#l7Lw!Q n\EM(E"0Y0!I7 Pwwwpw  p  V =+++ AA !#$%&'() a7 @@P@ P   =→=−==→==→==+ cbacbbaay x jx4QG!-&!IAW!/!-(-d  bd  7 28 28 28 28 28  8  %&'(  p  @ V   P   P   9                 ==↔ =−=↔ −−+=↔ −+= yx caNFNF NFNFNFNFNFNFFF NFNFNFNFFF n\ELP.M(E"0Y0!7         −−         −         −           2  P @   2  P @   2  P @   2  P P NNNN 28 28 28 ,!#$%&'() j5?!-;!- 22  Mquađi∆ #L#4 22 → u @ 22P2@22  −=       −= →→→ uAMAM j!-S1 ! ∆ I1<l 8 9 2 2  =       =∆ → →→ u uAM Ad j*(-1ad0 8 P    ===→ AHAFAE n\Ea2d0NY0f12 tl 8 P #5?!-;!- ∆ 2!"!(a2dI!-O'(O7          =+++− = = = 8      zyx z ty tx 28 28 28 l 8   0E/((a#dI7            = + = + = ∨            = − = − =  8 P 8   8 P 8  z y x z y x 28 -9 !#$ %&'() j34eXlDjE 2 Ryx ∈ <O      = +=−+ ↔ PP  xyi iyiyx       = = ↔        −=∨= = ↔    P  P  P y x x y x y x y n\E4eY!+I7 iz   P  P += 28 28 28  9  ,   *+   !"!##$%&'(    x y x − = −  n 456!-/+! 40E !'(2 B!-S.s@ ! 40E ! K!-   *+  3456!-/+!  w !  9  !  !      x x x x π π + + = + +  3O456!-/+!7 P        x x y x y x y x xy  − + =   − + = −   *+;*A!A4f!7sl P  (! I!   x x dx x π ∫ *+-; +!L4Z1LE1I(-#0W!-1#=1l(2N"!I (-f!y!Z<(N4;!-Z1#Z1z!-#=N4;!-E-L9   *A!W!'(-L-,((N4;!-Z1#Z *+-;(22IQ56!-M()!(jjle!-!/K!-7   a b b c c a ab c bc a ca b + + + + + ≥ + + + ./  !"# < 1213456711+8 *+- */!-N4;!-(HDE.1@#5?!-;!- ∆ 7DjEjPl *+(.05?!-;!- ∆ (5?!-;!-1# ∆ U4#=!(0-L P8   */!-BW!--(!#=O(HDEX2.R@@ #(5?!-;!-    7    x y z d + = = − − #  P  {7   8 x y z d − − = = e!-!7.R2Q2Q|z!-!K/"!N4;!-n 456!-/+!N4;!- L *+- 3456!-/+!7    P  P  P  I- I- x x x x x Log x x x + + + + =  121345671*52 *+-9 */!-N4;!-(HDE5?!-/C!    7 C x y+ = 25?!-;!-   7 d x y m+ + = *+ m .  C ^  d 1#(QO!A(-1HI=! !:  w o  o g   */!-BW!--(!#=O(HDEX2(N4;!-7 ]7DkEjXjl2}7DkEjXjl2t7DjEkXjl #5?!-;!-  ∆ 7   − −x l  +y l  z 3  ∆ I-(0E !'(]#} n 456!-/+!5?!-;!-Q#0W!--L#=t#^(5?!-;!-  ∆ 2  ∆  *+-9 3:456!-/+!7I- D I-  V D kw ≤  , *+=> ?&@+5 &'(  ~*\4D&!7 { } i D = ¡ ~*A!   {    y x D x − = < ∀ ∈ − <!-& !/"!B!-  @−∞ # @ +∞ ~<BW!-L/& ~3=!  + → = +∞ x lim y  x Limy − → = −∞  x Lim y →+∞ =   x Lim y →−∞ = %&LO\!e!-7Dl2O\!!-(!-El ~!- !"! D −∞  +∞ E|  E  +∞  −∞   ~n$%& 8 8 8 8  ~* 40E !'(.    @    M x f x C∈ L456!-/+!     {    y f x x x f x= − + <(E           x x y x x+ − − + − = ~ ~!-S.s@ ! 40E !~K!-    P        x x − ⇔ = + −  -5U!-O  x = #  x = ~ 40E !Y!+7  x y+ − = # 8 x y+ − = 8 8 8 8  ~ !•456!-/+!)56!-56!-#=  p     !     9  9 c x x c x π − + + + =    8      9 c x c x π π ⇔ + + + + =       8     9 9 c x c x π π ⇔ + + + + = 35U    9  c x π + = − #    9 c x π + = − I ~3    9  c x π + = − 5U!-O   x k π π = + # 8  9 x k π π = − + 8 8 8 8  ~ !•O56!-56!-#=            x xy x y x y x xy  − = −   − − = −   ~N€!4G   x xy u x y v  − =   =   2(5UO    u v v u  = −  − = −  ~3O/"!5U!-O0@#I@#@ ~*SL-5U!-OD@EI@#@ 8 8 8 8  ~NlD *A!Ql!DQD2•\!Dl+l2 P x π = +   t = *SL         I! I!t t I dt dt t t = − = ∫ ∫ ~N   I! @u t dv dt t = =    @du dt v t t ⇒ = = − Z0E/(           I! I!       I t dt t t t = − + = − − ∫ ~ F0    I!   I = − −  8 8 8 8 P ~n$+! ~3<I/0!-.2e!-!  SH ABC⊥ ~•&!‚!--L-,((N4;!-Z12Z1#=NEI   9SEH SFH= = ~T HK SB⊥ 2I\4I0\!0E/(-L-,((N4;!-Z1#Z K!- HKA  8 8  V  ~[\4I0\!#A!5U1l1l(2   a HA = 2   (! 9  a SH HF= = ~*(-Z<#0W!-<L         KH a HK HS HB = + ⇒ = ~*(-1<#0W!-<L    (!    a AH AK H KH a = = =     AK H⇒ =  8 8 8 ~ !•       a b c c ab c ab b a a b + − − = = + + − − − − ~*SL             c b a VT a b c a c b − − − = + + − − − − − − h(22Q56!-#(jjl!"!(220B!-@lv(22 Q56!- ~4QG!-:;!-eW(Q56!-(5U                 c b a VT a b c a c b − − − ≥ − − − − − − l4 ;!-eDE/(B#yB   a b c= = = 8 8 8 8 9( ~ ∆ L456!-/+!(     x t y t = −   = − +  #L#4  @u = − ur ~10 ∆    @   A t t⇒ − − +  ~*(L1@ ∆ lP8     @   c AB u⇔ = uuuur ur      AB u AB u ⇔ = uuuur ur ur   8  9V 89 P8    t t t t⇔ − − = ⇔ = ∨ = − ~.Y!+I    P    @ 2  @      A A− − 8 8 8 8 9( ~QF0(  @ @M − #L#4  @ @ u = − − uur Q|F0(  @@PM #L#4  @@8u = uur ~*(L   @  P@ p@Pu u O   = − − ≠   uur uur ur 2   @@PM M = uuuuuuur •ƒ     @  9 P u u M M   = − + =   uur uur uuuuuuur Q#Q|%!-4;!- ~3]IN4;!-e(Q#Q|lv]L#4 @@ n = − ur #F0( R  !"!L456!-/+!   x y z+ − + = ~h„:E.R@@0o]2SL(L4 8 8 8 8 w( ~0BO!7Dv   [...]... 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 WWW.ToanCapBa.Net 31 B thi i hc 2012-2013 WWW.ToanCapBa.Net 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 Giải hệ phơng... 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, 6 cách chọn c, 5 cách chọn d, 4 cách chọn e, 3 cách chọn f ở đây 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)... cho tam giác ABC biết A(2; - 3), B(3; - 2), có diện tích bằng 3 và trọng tâm thuộc đờng thẳng : 3x y 8 = 0 Tìm tọa độ đỉnh C 2 Câu VII.a (1 điểm) Từ các chữ số 0,1,2,3,6,7,8,9 có thể lập đợc bao nhiêu số tự nhiên có 6 chữ số đôi một khác nhau ( chữ số đầu tiên phải khác 0) trong đó phải có chữ số 7 log 1 Câu VIII.a (1 điểm) Tìm a để bất phơng trình sau có nghiệm: x 2 +1 > log 1 ( ax + a) 3 B.Theo... bằng 2 khi x0 = 0 hoặc x0 = -2.Nh vậy ta có hai II (2,0 điểm) 0,25 1.(1,0 điểm) Giải hệ Điều kiện: x -1, y 1 Cộng vế theo vế rồi trừ vế theo vế ta có hệ 0,25 điểm cần tìm là (0;1) và (-2;3) x+1 + x+6 + y 1 + y+ 4 = 10 x+6 x+1 + y + 4 y 1 = 2 WWW.ToanCapBa.Net 33 0,25 B thi i hc 2012-2013 WWW.ToanCapBa.Net Đặt u= x + 1 + x + 6 , v = y 1 + y + 4 Ta có hệ u + v= 10 u= 5 v =5 5 5 + =2 u... khụng theo cỏch nh trong ỏp ỏn, gv vn cho im ti a tng ng nh trong ỏp ỏn ) ẩ THI TUYN SNH I HC 5 MễN TON Thi gian:180 phỳt (Khụng k thi gian phỏt ) WWW.ToanCapBa.Net 21 B thi i hc 2012-2013 WWW.ToanCapBa.Net I PHN CHUNG CHO TT C TH SINH (7,0 im) Cõu I (2,0 im) Cho hm s y = x3 2x2 + (1 m)x + m (1), m l s thc 1 Kho sỏt s bin thi n v v th ca hm s khi m = 1 2 Tỡm m th ca hm s (1) ct trc honh ti 3 im... tng ng vi log 3 (9x 72) x 0.25 9x 72 3x x 3 8 x x2 3 9 *Kt lun tp nghim : T = (log 9 72; 2] 0.25 0.25 THI TUYN SINH I HC 3 Mụn: TON (Thi gian lm bi 180 phỳt, khụng k thi gian phỏt ) PHN CHUNG CHO TT C TH SINH(7,0 iờm) Cõu I ( 2,0 im): Cho hm s y = 2x 4 x +1 1 Kho sỏt s bin thi n v v th (C) ca hm s 2 Tỡm trờn th (C) hai im i xng nhau qua ng thng MN bit M(-3; 0) v N(-1; -1) Cõu II (2,0... sin() ) = 8 z = 1 i 2 z + iz = 4 4i + i(4 + 4i) = 8(1 + i) z + iz = 8 2 THI TUYN SINH I HC 6 MễN TON(180 phỳt Khụng k thi gian phỏt ) A.PHN CHUNG CHO TT C CC TH SINH (7 im): y = x 3 3mx 2 + 3(m 2 1) x m3 + m (1) Cõu I (2 im): Cho hm s 1.Kho sỏt s bin thi n v v th ca hm s (1) ng vi m=1 2.Tỡm m hm s (1) cú cc tr ng thi khong cỏch t im cc i ca th hm s n gúc ta O bng 2 ln khong cỏch t im cc... y x log 3 12 + log 3 x = y + log 3 y 3 y = 2 x y = 2 log 4 2 3 1 THI TUYN SINH I HC 4 (Thi gian lam bai 180 phỳt khụng kờ thi gian phỏt ) PHN CHUNG CHO TT C CC TH SINH (7,0 im) Cõu I: (2,0 im) Cho hm s y = x3 3mx2 + (m-1)x + 2 1 Chng minh rng hm s cú cc tr vi mi giỏ tr ca m 2 Xỏc nh m hm s cú cc tiu ti x = 2 Kho sỏt s bin thi n v v th (C) ca hm s trong trng hp ú Cõu II: (2,0 im) 1 Gii phng... điểm) * Tập xác định: D = R\{ - 1} * Sự biến thi n - Giới hạn và tiệm cận: xlim y = xlim y = 2 ; tiệm cận ngang: y = 2 + WWW.ToanCapBa.Net 32 0,25 B thi i hc 2012-2013 WWW.ToanCapBa.Net lim y = +; lim + y = ; tiệm cận đứng: x = - 1 - Bảng biến thi n Ta có y ' = x - y x ( 1) 1 < 0 với mọi x - 1 ( x + 1) 2 -1 + + 2 0,5 + + y x ( 1) 2 - Hàm số đồng biến trên mỗi khoảng (- ; -1) và ( -1; + ) * Đồ thị... SABCD cú ỏy ABCD l hỡnh vuụng cnh a, tõm O Cnh bờn SA vuụng gúc vi mp (ABCD) v SA = a; M l trung im cnh SD WWW.ToanCapBa.Net 17 B thi i hc 2012-2013 WWW.ToanCapBa.Net a) Mt phng () i qua OM v vuụng gúc vi mt phng (ABCD) ct hỡnh chúp SABCD theo thit din l hỡnh gỡ? 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