NGÂN HÀNG ĐỀ KIỂM TRA- TOÁN 11- CHƯƠNG TRÌNH CHUẨN STT Mã câu hỏi Ý, thời gian Nội dung Điểm        3 3 3 2 5 lim 1 2 n n n + + +     5 2.3 lim 4 3.5 n n n n + −    3 2 3 3 3 2 5 3 3 2 5 3 lim lim . 1 1 2 2 2 n n n n n n + + + + = = + +    3 1 2. 5 2.3 1 5 lim lim . 4 3.5 3 4 3 5 n n n nn n   +  ÷ +   = = − −   −  ÷           2 3 2 lim 1 n n n n − + + − +    1 1 ( 2) 3 lim ( 2) 3 n n n n+ + − + − +   3 2 2 2 3 1 2 3 2 lim lim 0. 1 1 1 1 n n n n n n n n n − + + − + + = = − + − +    11 1 2 1 ( 2) 3 1 1 3 lim lim . ( 2) 3 3 3 2 1 3 n n n nn n ++ +     − +    ÷ − +     = =   − +   − +    ÷          ( ) 1 3 3 3 3 3( 1) 2 4 2 2 2 2 n n S + − = − + − + + +   !"#$%!&'( 1 1 3 , 2 2 q u= − = )*+, ( ) 1 3 3 3 3 3 3( 1) 3 2 . 1 2 4 2 2 2 1 2 2 1 2 n n S + − = − + − + + + = = + +       2 2 1 1 lim 3 2 x x x x →− − + +   2 2 1 1 1 1 ( 1)( 1) 1 lim lim lim 2. 3 2 ( 1)( 2) 2 x x x x x x x x x x x x →− →− →− − + − − = = = − + + + + +       2 1 2 3 lim 1 x x x → − + −   2 2 1 1 1 1 2 3 4 ( 3) lim lim 1 ( 1)(2 3) ( 1) lim ( 1)( 1)(2 3) 1 1 lim . 8 ( 1)(2 3) x x x x x x x x x x x x x x x → → → → − + − + = = − − + + − − = − + + + − = − + + +    -    3 2 4 2 3 5 3 9 lim 8 9 x x x x x x → − + + − −   3 2 2 4 2 2 2 3 3 2 3 5 3 9 ( 3) ( 1) lim lim 8 9 ( 1)( 9) ( 3)( 1) lim 0 ( 1)( 3) x x x x x x x x x x x x x x x x → → → − + + − + = = − − + − − + = + +   .  /  3 2 4 2 lim 2 x x x → − −   ( ) ( ) ( ) ( ) ( ) 2 3 3 3 3 2 2 2 3 3 2 2 2 2 3 3 3 3 2 2 3 3 ( 4 2) 4 2 4 4 4 2 lim lim 2 ( 2) 4 2 4 4 4 8 4( 2) lim lim ( 2) 4 2 4 4 ( 2) 4 2 4 4 4 1 lim . 3 4 2 4 4 x x x x x x x x x x x x x x x x x x x x x x x → → → → →   − + +   −   = −   − + +     − − = =     − + + − + +         = =   + +        0   12!345"6% 2 1 Õu 1 ( ) ¹i 1. 1 2 Õu 1 x n x f x t x x n x  − ≠ −  = = − +   − = −   1*789:7;)<=;>7'" 2 1 1 1 1 1 ( 1)( 1) lim ( ) lim lim lim( 1) 2 ( 1) 1 1 x x x x x x x f x x f x x →− →− →− →− − − + = = = − = − = − + + *+,"6%!34:7;)   ?   @6AB6,C"6%!34:7; 3 4 1 Õu 1 ( ) . 1 Õu 1 x n x f x x m n x  + − ≠ −  =  +  = −    1 1 1 1 3 4 1 3 4 1 lim ( ) lim lim 1 ( 1)( 3 4 1) 3 3 lim 2 3 4 1 x x x x x x f x x x x x →− →− →− →− + − + − = = + + + + = = + + <=;>76)DE ,C"6%!34:7;F'"GF67H)       /96$IJA@#6KL6KF+M=; N> 5 3 2 5 1 0.x x− − =  O<=:>7 5 3 2 5 1x x− −  <=;>7<=>7; P+,<=;>)<=>Q=> <=:>!34A383!34A3R;NS=> T=>'"=>$IJA@<=:>7#6KL6A3F+M =;N>9!"KF+M=;N>)       ,+"65"6% (2 1)(4 3)y x x= + − )   ' (2 1)'(4 3) (2 1)(4 3)' 1 2 8 1 (4 3) (2 1) . y x x x x x x x x x x = + − + + − − = − + + =      ,+"65"6% 3 4 . 4 5 x y x − = +   2 2 2 (3 4)'(4 5) (3 4)(4 5)' ' (4 5) 3(4 5) (3 4)4 31 . (4 5) (4 5) x x x x y x x x x x − + − − + = + + − − = = + +      ,+"65"6% 2 1 os 2 x y c= +   ' 2 2 2 2 2 1 ' 1 os 2 2 1 os 2 1 .2 os (cos )' 2 2 2 1 os 2 1 s inx .2 os ( sin ).( )' . 2 2 2 2 1 os 4 1 os 2 2 x y c x c x x c x c x x x c x x c c   = + =  ÷   + + − = − = + +       /+,IU+=/> 3 ( ) .y f x x = = DV$IJA@V$ V5 =/>VV$ V,++',IUW 7;:)  D@V$ V5=/>++',IUW 7;:3L% F7;)  *+, 2 0 0 2 0 3 1 3 3x x x − = − ⇔ = ⇔ = ± F 0 0 0 3 3 × 3 µ ' 1 3 x th y v y= = = = − $IJA@V$ VIJ9!" 2 3y x= − + F 0 0 0 3 3 × 3 µ ' 1 3 x th y v y= − = − = = − $IJA@V$ VIJ9!" 2 3.y x= − −     / /+,IU+=/> 2 ( ) 2 3.y f x x x= = − + DV$IJA@V$  V5=/>VV$ V,'(',IUW:X 7)  D@V$ V5=/>'(',IUW:X 73L% F7 *+, 0 0 2 2 4 3x x− = ⇔ = F 0 0 3 × 6x th y= = $IJA@V$ V5=/>!" 7:;-)    -  Y /+9PL/*) /96 AB CD AD CB+ = + uuur uuur uuur uuur   V,'VA AB CD AD DB CB BD+ = + + + uuur uuur uuur uuuur uuur uuuur = >AB CD AD CB DB BD+ = + + + uuur uuur uuur uuur uuuur uuuur AB CD AD CB+ = + uuur uuur uuur uuur    .  Y /+@$Z)/*Z ⊥ =/*>, /*!"@ '()[\]^!_!I`!"A,C65Z'"Z*)   /96 = >BC SAB⊥ / /96]^ ⊥ =Z/>  /96 = >BC SAB⊥ = > BC AB BC SAB BC SA ⊥  ⇒ ⊥  ⊥   / /96]^ ⊥ =Z/> = > BD SA BD SAC BD AC ⊥  ⇒ ⊥  ⊥  => ]^HH*=> T=>'"=> A]^ ⊥ =Z/>  0  Y /+9PL/*' = >AB BCD⊥ '"7N, /*!"6 ,a)[\b!"A,C65/*)@6+c HA uuur '" BH uuur  [+c HA uuur '" BH uuur b7  · ·       a AHB AHB a = = ⇒ = = HA uuur N BH uuur >70  d  7     ?  Y /+9PL,a/*e)bf '(I  A B C D B D H 2a a C A Z  / *  ] ^ g h   )AB AD uuur uuur . / )AB CM uuur uuuur A+,]!"A,C6*)      ) ) )+= ) >   ) )+-   AB AD AB AD AB AD a a a a = = = = uuur uuur uuur uuur uuur uuur   /        ) = > ) )     ) + ) )+- ) ) )         AB CM AB AM AC AB AM AB AC a a a a a a a a a = − = − = − = − = − = uuur uuuur uuur uuuur uuur uuur uuuur uuur uuur      Y /+@!E$$IJ/*)YY/Y*Ye)i ,IUW /'"*YNY'"*YN/Y'"**Y)  X*+Y/YHH/3i/'"*YY!" iY/Y'"Y*Y'"e   ) X6Y*Y,a3i *Y'"Y!"  - X[i/Y'"**Y!"i/Y'" Y 3     A   A C a AA a ϕ ϕ = = = ⇒ =       Y /+@$Z)/*, !"@'()/3Z'( '6$=/*>)A3Z!# ,C6]'"A3Z/!# ,C6^++ SM SN SA SC = )   /96Ae6O3@$!"6'()  / /96 = >MN SBD⊥ )   *+Z'(', 3 SB AB SB BD SAB⊥ ⊥ ⇒V '" SBDV '( ) *+/*!"@'(3 NBA AD BC CD⊥ ⊥ j+,B !,IU'( NSA AD SC CD⊥ ⊥  A SADV '('" SCDV '(/)    / *+ = >SB ABCD SB AC⊥ ⇒ ⊥ '" = >AC BD AC SBD⊥ ⇒ ⊥   C D B A M A' B' C' B D C A D' N M O D B C A S 6OFP+ HH = > SM SN MN AC MN SBD SA SC = ⇒ ⇒ ⊥    Y /+@$Z)/*, !"@'(e)/3 Z'('6$=/*>)[iZ'"6$=/*>!"  - )   1,BiZ*'"6$=/*>T,,KP"3 @$)  / hk BK SO ⊥ l!"+5/'"*96 = >BK SAC⊥   D@*!"@V5Z*A36O,  3iZ*'", !" ¼  -SDB =   - )  -SB BD a a= = =      +-  BD a SD a= = =       - . .SA SB AB a a a SA a SC= + = + = ⇒ = =     / *+ = >AC SBD⊥ j+96A33 AC BK ⊥ D@ BK SO ⊥ j+MV = >BK SAC⇒ ⊥     Y /+@$Z)/*, !"@'('"Z ⊥ =/*>)V Z7 a '"7)   /966O35@$!"6'()  * i,IUWZ/)   D@ ( ) SA ABCD⊥  3  SA AB⊥  SA AD⊥  3    6    SAB SAD !"6'()  ( ) SA CD CD SAD CD SD CD AD ⊥  ⇒ ⊥ ⇒ ⊥  ⊥  36 SCD !"6'()IJm6 SBC !"6 '()    *  HHAB CD 3 · ( ) · ( ) ·  AB SC CD SC SCD= = ) D@Z7 a '"7/*73Z*7 a )A+6'( Z/* Z*   / 7 7 7  /*  )DE  · ( )  -AB SC = o    O D B C A S K   Y /+@$,aZ)/*l!"65/*Z7 a  7)[\g!"A,C65/*)   /96/*⊥=Zlg>  * %,+i6O$W=Z/*>'"=/*>   /*⊥=Zlg> Zg⊥/*=Zg!"A VFkT,G6Z/*> D"lg⊥/*=lg!"A VFkT,G6l/*> *+,/*⊥=Zl]>   * =Z/*>∩=/*>7/*Zg⊥/*'"lg⊥/*3i=Z/*>'" =/*>!"Zgl) A+6'(Zl/Zl  7Z/  ;l/  7  H A+6'(Zlg Zgl7Zllg7 ¼     . .-n   a a SIO = ⇒ =       Y /+@$Z)/*, /*!"@iE6l)Z =/*>  *  Z )⊥ = = =   /966O3!"6'()  [\b!"A,C65*)/96lb = >⊥ SAD ) / F+MTl,V=Z*>  Z ⊥ =/*> ⇒ Z ⊥ NZ ⊥ *  !"@V5ZA3=/*> ]"/ ⊥ 3/ ⊥ Z b 6Z/'( /]IJm6Z*/'(*      lb ⊥ * lb ⊥ Z ⇒ lb ⊥ =Z*>   / )h+MTl,V=Z*>!"lb  lb7H7H   A B D C O S I H H O D B C A S . NGÂN HÀNG ĐỀ KIỂM TRA- TOÁN 11- CHƯƠNG TRÌNH CHUẨN STT Mã câu hỏi Ý, thời gian Nội dung Điểm    . +   3 2 2 2 3 1 2 3 2 lim lim 0. 1 1 1 1 n n n n n n n n n − + + − + + = = − + − +    11 1 2 1 ( 2) 3 1 1 3 lim lim . ( 2) 3 3 3 2 1 3 n n n nn n ++ +     − +    ÷ − +     =. 1) 3 3 lim 2 3 4 1 x x x x x x f x x x x x →− →− →− →− + − + − = = + + + + = = + + <=;>76) DE ,C"6%!34:7;F'"GF67H)       /96$IJA@#6KL6KF+M=; N> 5