Đề, đáp án ĐH toán khối A, A1 2013

 -   32 y x 3x 3mx 1 (1)      a)    )  1 tanx 2 2sin x 4         4 4 22 1 1 2 2 ( 1) 6 1 0                  x x y y x x y y y (x, y  R). Tính tích phân 2 2 2 1 1 ln    x I x dx x Cho  0 ABC 30 ,  S.ABC  Câu    Cho các s           2 (a c)(b c) 4c            3 3 2 2 33 32a 32b a b P (b 3c) (a 3c) c         Thí sinh chỉ được làm một trong hai phần (phần A hoặc phần B) A.    2x y 5 0   và A( 4;8)  B qua C, N là hình  -4).                x 6 y 1 z 2 : 3 2 1         và vuôn    sao cho AM = 2 30 .                     :x y 0    10    AB = 42       Trong không gian         (P):2x 3y z 11 0       2 2 2 (S):x y z 2x 4y 2z 8 0          Cho  z 1 3i   5 w (1 i)z .  Câu 1: a) m= 0-x 3 + 3x 2 -1 -3x 2 +  x = 0 hay x = 2; y(0) = -1; y(2) = 3 lim x y    và lim x y    x  0 2 +   0 + 0  y + 3 -1     - 3 y" = -6x +    : b. -3x 2 + 6x+3m m= 2 2xx =g(x)     0, 0;x     m 2 2xx   0;x        2 0 min 2 , 0; x m x x x          11mg   Câu 2 : 1+tanx=2(sinx+cosx)  cosx+sinx = 2(sinx+cosx)cosx   sinx+cosx=0 hay cosx = 1 2  tanx=-1 hay cosx = 1 2  2, 43 x k hay x k k          Câu 3 :  1x   22 2 1 6 1 0     x y x y y   2 1 4 0    x y y     2 4 1 *   y x y  0y 4 4 1 1 2     x x y y        44 4 4 1 1 1 1 1 1 **        x x y y  4 11tt   thì f ) Nên (**)  f(x) = f(y 4 + 1)  x = y 4 + 1  4y = (y 4 + y) 2 = y 8 + 2y 5 + y 2  74 01 24 yx y y y           0 1 y y      (vì g(y) = y 7 + 2y 4 ) (x; y) = (1; 0) hay (x; y) = (2; 1). Cách khác :   22 2 1 6 1 0     x y x y y  x = -y + 1 2 y vì x  1  x = -y + 1 2 y y x 2 -1 3 0  1  0 và v = y 4   44 22u u v v      4 2tt )  f(u) = f(v)  u = v  x  1 = y 4 Câu 4 : 2 2 2 1 1 ln x I xdx x    t=lnx   , , (1) 0, 2 ln2 t dx dt x e t t x        ln2 0 tt I t e e dt       u=t , tt du dt dv e e       tt v e e    I = ln2 ln2 0 0 ( ) ( ) t t t t t e e e e dt        = 5ln2 3 2  Cách khác :  u ln x dx du x  dv = 2 22 x 1 1 dx (1 )dx xx   1 vx x    2 2 1 1 1 1 dx I x ln x (x ) x x x          2 1 51 ln2 (1 )dx 2x      2 1 51 ln2 (x ) 2x    51 ln2 (2 ) 22    53 ln2 22  Câu 5.   (ABC) và SH = 3 2 a  BC=a, 3 , 22  aa AC AB 3 1 1 3 3 3 2 2 2 2 16 a a a a V     ,  HI=a/4, 3 2  a SH  SI thì HK  (SAB), ta có 22 2 1 1 1 3 52 3 4 2 a HK HK a a               = 2HK = 2 3 3 52 13  aa Câu 6. G   1 1 4 ab cc              a c ; y = b c thì (x + 1)(y + 1) = 4  S + P = 3 P = 3  S P = 3 3 22 32 33 xy xy yx                3 22 8 33 xy xy yx        = 3 2 32 8 39 2 S S P S SP       = 3 2 3 2(3 ) 8 3 (3 ) 9 2 S S S S SS           S A B C H I = 3 3 2 5 6 1 88 2 12 2 22 S S S S S S              = 3 ( 1) , 2 2 S SS    1) 2  1 2 > 0, S  2  P min = P (2) = 1  2  Câu 7a. C(t;-2t-5)  4 2 3 ; 22        tt I Ta có: IC 2 = IA 2 , suy ra t =1 -7) -4;-7) Câu 8a. Ptmp (P)   -3; -2; 1). -3(x  1)  2(y  7) + z  3 = 0  3x + 2y  z  14 = 0   M (6 -3t; -1  2t; -2 + t) YCBT  (5  3t) 2 + (-8  2t) 2 + (-5 + t) 2 = 120  14t 2  8t  6 = 0  t = 1 hay t = 3 7  -3; -1) hay ( 51 7 ; 1 7  ; 17 7  ). Câu 9a.   : 3.6.5=90     Câu 7b. Cos(AIH) = 1 5 IH IA   IH = 2  IH = 4 2  Oy (0; y) MI  AB  MI : x + y + c = 0 ; M (0;-c) MH = d (M; ) = 2 c = 4 2  c = 8 hay c =-8 I (t; -t  8) hay (t; -t + 8) d (I; ) = 8 2 2 tt IH    t = -3 hay t = -5 -3  I (-3; -5); t = -5  I (-5; -3)   2 + (y + 5) 2 = 10 hay (x + 5) 2 + (y + 3) 2 = 10. Câu 8b. (S) có tâm là I (1; -2; 1) và R 2 = 14.  2(1) 3( 2) 1 11 14     = 14 = R  Pt (d) qua I và   : 1 2 1 2 3 1 x y z    , T  (d)  T (1 + 2t; 3t  2; 1 + t) T  (P)   Câu 9b. r = 13 = 2; tg = 3  = 3    2(cos sin ) 33 i   M A B I H  z 5 = 5 5 1 3 32(cos sin ) 32( ) 3 3 2 2 ii      w = 32(1 + i) 13 () 22 i = 1 3 1 3 32( ) 32 ( ) 2 2 2 2 i    16 16 3  16 16 3 .   TP.HCM) .  (ABC) và SH = 3 2 a  BC =a, 3 , 22  aa AC AB 3 1 1 3 3 3 2 2 2 2 16 a a a a V     ,  HI=a/4,