Đề cương ôn thi toán 11 kỳ II (có đáp án)

   TRƯƠ ̀ NG PT DTNT ĐĂK HA ̀           ! "##$%&'()%  &* ĐÊ ̀ ĐA ́ P A ́ N Câu 1:+', ! -. ! &,&'+ ! ' &/ )  "01(&/2 & *3)"4 ! 52 # 632 7 68 #8 1 ! '9  :39"4  ;* < ! &2 = > 81 ! '9  $:#39"4  ;* < ! &5  &/#. ! %  &/9,  25"4&'2  % ', ! -. ! &,&9+ ! #8%'+ !    7 7 # # 8 u u u q q u = ⇒ =   ?  q⇒ = = q⇒ = @<  ' &/)  "01(&/* A = # 8u u q⇒ = A = 8 #u⇒ = = 8%'+ ! B # # #  * #  S − = − # #?* ?A # − = = − Câu 2:< ! &'% ! '/"( ! "%  &.%2B #81 ! '9  :#3C9"4  ;*   A  D";  7 n n n − + 81 ! '9  :3C9"4  ;* ( )  D"; n n n+ − #8%'+ ! B     A A  D"; D"; 7  7  n n n n n − − = + + A 7  = = 8%'+ !  ( )  D"; n n n+ − ( ) ( ) ( )    8 D"; n n n n n n n n n + − + + = + + ( )  D"; n n n n = + + # D"; # # # #  n =   + +  ÷   = Câu 3:< ! &'% ! '/"( ! "%  &.%2B #81 ! '9  :#3C9"4  ;*  7  D"; 7 x x x →− − + 81 ! '9  $:#3C9"4  ;*   C A D";  x x x x → − + − #8%'+ ! B  7 7   7* 7* D"; D"; 7  7* x x x x x x x →− →− − − + = + +  7 D"; 7* A x x →− = − = − 8%'+ ! B ( )     * 7 C A D"; D";   x x x x x x x x → → − − − + = − −  D"; 7* # x x → = − = − Câu 4:< ! &'% ! '/"( ! "%  &.%2B #8 1 ! '9  :#3C9"4  ;*    7 D"; 7 x x x x →+∞ + − 81 ! '9  $:39"4  ;*  7 D";  x x x − → + − #8%'+ ! B    7   7 D"; D"; # 7 7 x x x x x x x →+∞ →+∞ + + = − −  7 = − 8%'+ ! B  D"; 7* C  x x − → + = >  D"; *  x x − → − = :EFG( ! ";+  "EF +9+ !   7 D";  x x x − → + = −∞ − Câu 5 :+%  ;. !   ? :   *  7 :  x khix f x x x khix  − <  = −   − ≥  HI ! 55< ! &D"4&52  ''2  %%  ;. ! 5%  "E6 %'+ !     ? D";  * D";  x x x f x x − − → → − = −  D"; * ? x x − → = + =   D";  * D";7 * ? x x f x x + + → → = − = J*6? @<     D";  * D";  * * ? x x f x f x f − + → → = = = &4&%  ;. ! D"4&52  '5%  "E6 Câu 6:+%  ;. !   :   * #:  x khix f x x khix  < =  + ≥  HI ! 55< ! &D"4&52  ''2  %%  ;. ! 5%  "E6 %'+ !     D";  * D";  x x f x x − − → → = =   D";  * D"; #* # x x f x x + + → → = + = @<     D";  * D";  * x x f x f x − + → → ≠ &4&%  ;. ! /"% ! &9+%  &5%  "E6 Câu 7:+%  ;. !   : #  * #: # ax khix f x x x khix + ≥  =  + − <  HI ! 55< ! &D"4&52  ''2  %%  ;. ! 5K4& %  ;. ! JE*E% ! '9"  &5K4& @( ! "EF#%  ;. ! JE*6E  LE#D"4&52  '5K4& ( ) :#−∞ @( ! "EM#%  ;. ! JE*6%ELD"4&52  '5K4& ( ) #:+∞ %  "E6#5%'+ ! B  # # D";  * D"; #* # x x f x x x − − → → = + − = # # D";  * D"; *  x x f x ax a + + → → = + = + J#*6%L L4 ! 2%6#5<   # # D";  * D";  * #* # x x f x f x f − + → → = = = 4&%  ;. ! D"4&52  '5%  "E6#.2NK%%  ;. ! D"4&52  '5K4& L4 ! 2% ≠ #5<   # # D";  * D";  * x x f x f x − + → → ≠ 4&  %  ;  . !  /"% ! &  9+%  &  5%  "  E  6  #  .2N  K%  %  ;  . !  D"4&  52  '  5K4& ( ) ( ) :# #:−∞ ∪ +∞ Câu 8:+%  ;. !   A  : 7  * 7 : 7 x x khix f x x khix  + + ≠ −  = +   = −  HI ! 55< ! &D"4&52  ''2  %%  ;. ! 5K4& %  ;. ! JE*E% ! '9"  &5K4& LK4&; O"P+%  &/ ( ) : 7−∞ − G%   ( ) 7:− +∞ %  ;. !   A  7 x x y x + + = + E% ! ' 9"  &&4&D"4&52  '8 L%  "E675%'+ ! B  7 7 A  D";  * D"; 7 x x x x f x x →− →− + + = + ( )  7 7 D"; 7 x x x →− + = + 7 D"; 7*  x x →− = + = J7*6 @<   7 D";  *  7* x f x f →− ≠ − &4&%  ;. ! /"% ! &9+%  &5%  "E67 @,  N%  ;. ! 9% O '+D"4&52  '5K4&'% ! 'P+%  &/ ( ) : 7−∞ − 3 ( ) 7:− +∞ G%  /"% ! & 9+%  &5%  "E67 Câu 9:+%  ;. !  7    : #  * #  #: # x x x khix f x x x khix  − + − ≠  = −   + =  HI ! 55< ! &D"4&52  ''2  %%  ;. ! 5%  "E6# %'+ !  7  # #   D";  * D"; # x x x x x f x x → → − + − = −  #  * #* D"; # x x x x → + − = −  # D"; * 7 x x → = + = J#*67 @<   # D";  * #* 7 x f x f → = = &4&%  ;. ! D"4&52  '5%  "E6# Câu 10:1 ! &/;"&-1(&/5K<  & E 7 QAEQ#6 + ! 7&/"4  ;5K4&P+%  &/:* R  5JE*6E 7 AE# %  ;. ! JE*E% ! '9"  &5K4& %'+ ! BJ*6CJ#*67 J*6#J*67 @<  J*8J#*6#CF&4&-1(&/5K<  &JE*6'+ ! < ! 5&, ! 5;  5&/"4  ; 5K4&:#* J#*8J*67F&4&-1(&/5K<  &JE*6'+ ! < ! 5&, ! 5;  5&/"4  ; 5K4&#:* J*8J*67F&4&-1(&/5K<  &JE*6'+ ! < ! 5&, ! 5;  5&/"4  ; 5K4&:* @,  N-1(&/5K<  &JE*6'+ ! < ! 5&, ! 57&/"4  ;5K4&P+%  &/:* Câu 11:1 ! &/;"&-1(&/5K<  & 7E 7 QAE  L#AEL76 + ! &/"4  ;5K% ! "0, ! 2 R  5JE*67E 7 QAE  L#AEL7 %  ;. ! JE*E% ! '9"  &5K4& %'+ ! BJ#*6C J*67 J#*6 @<  J#*8J*6CF&4&-1(&/5K<  &JE*6'+ ! < ! 5&, ! 5;  5&/"4  ; 5K4&#:* J*8J#*6=F&4&-1(&/5K<  &JE*6'+ ! < ! 5&, ! 5;  5&/"4  ; 5K4&:#* @,  N-1(&/5K<  &JE*6'+ ! < ! 5&, ! 5&/"4  ;5K% ! "0, ! 2&%2 Câu 1 2 : +%  ;. ! BN6E 7  L 7E  L# @"4 ! 5-1(&/5K<  &5"4 ! -52N4 ! &'2  % 9  5"  %  ;. ! 5%  "9"4  ;'+ ! +%  &9  E  6# %'+ ! BNS6AE  LAE 2NK%NS#*6# /+%  "K%N#*6A 4&-1(&/5K<  &5"4 ! -52N4 ! &'2  %9  5"  %  ;. ! 5%  "#:A*D%  B N6#E#*LA %NN6#EA Câu 1 3 :< ! &9%  +%  ;'% ! '%  ;. ! .%2B #81 ! '9  :3=C9"4  ;* JE*6E 7 LE  7EL# 81 ! '9  :#3C9"4  ;*  7  *  x f x x + = − #8 JSE*6AE  LE7 8 ( ) ( ) ( ) ( ) ( )   7 T8   T8  7 T *  x x x x f x x + − − − + = − ( ) ( ) ( )  8   7  x x x − − + = − 781 ! '9  $:#3=C9"4  ;* JE*6E85%&E ( ) ( )   ? 7 =  x x − − = = − − − 78 JSE*6#85%&ELE85%&E*S 65%&EL  '+. x x Câu 1 4 : +<  &'+ ! -8$ '+ ! 9% ! N$D%  <  &G2 &/G%  '+ !  *SA mp ABCD⊥ #8 1 ! '9  :9"4  ;* 1 ! &/  ;"&  SB BC⊥  G%  SD DC ⊥ 81 ! '9  $:#9"4  ;* +  "D%  /"%+9"4  ;%"91(  &/'I ! + G%  $3'1 ! &/;"& SODV D%  5%;/"% ! 'G2 &/ #8%'+ !   *SA mp ABCD SA BC⊥ ⇒ ⊥ G<    *BC ABCD⊂ #* %D%  "'+ !  AB BC ⊥ $D%  <  &G2 &/** 1  #*G%  * SB BC⇒ ⊥ 1(&/51   SA DC SD DC AD DC ⊥  ⇒ ⊥  ⊥  8%'+ !   *SA mp ABCD SA BD⊥ ⇒ ⊥ G<    *BD ABCD⊂ #* %D%  "'+ !  BD AC ⊥ $G%  D%  91(  &/'I ! +'2  %<  &G2 &/** 1  #*G%  * SO BD⇒ ⊥ %N SODV G2 &/5%  " Câu 1 5 : +51 ! 0"4  &$'+ ! 3$39 ";  5G2 &//+ ! '8 +  "    D%   9"4  ;  52  '  ;R  5 -R  &/$*  .%+  '+  *OH mp ABC⊥ 8  1 ! &/  ;"& KR  &/B #81 ! '9  :#3C9"4  ;*   *BC mp OAH⊥  #8%'+ ! B  *AO mp ABC AO BC⊥ ⇒ ⊥ G<    *BC ABC⊂ #* R  5P% ! '5I+/"%  52N4 ! 55%'+ !   *OH mp ABC⊥ .2NK% OH BC⊥ * 1  #*G%  *  *BC mp OAH⇒ ⊥ 8 I  'R ! 5$5%  "8 %;  /"% ! '    G2 &/  5%  "    '+ !    D%   01(  &/  '%+  &4&  5%  '+ ! B 81 ! '9  :#3C9"4  ;*      # # # # OH OA OB OC = + +    # # # OH OA OM = + #* I+',2#85%'+ !   *BC mp OAH BC OM⊥ ⇒ ⊥ %ND%  91(  &/'%+ 5K+&/5%;/"% ! '$G2 &/5%  "&4&5%'+ !     # # # OM OB OC = + * 1  #*G%  *     # # # # OH OA OB OC ⇒ = + + Câu 1 6 :+51 ! 0"4  &$'+ ! 5%; /"% ! '  $  G2 &/  5%  "  $3  *SA mp ABC⊥ #81 ! '9  :#3C9"4  ;* 1 ! &/;"&  *BC mp SAB⊥ 81 ! '9  $:#3C9"4  ;* +  "D%  91(  &/'%+'2  %5%;/"% ! ' $3D%  91(  &/'%+'2  %5%; /"% ! '  8 1 ! &/  ;"&  *SC mp AHK⊥ #8%'+ ! B  *SA mp ABC SA BC⊥ ⇒ ⊥ G<   *BC ABC⊂ *#*R  5P% ! '5I+ /"%   52N4 ! 5  5%  '+ !  BC AB⊥ @<  5%;/"% ! '$G2 &/5%  "$** 1  #*G%  *  *BC mp SAB⇒ ⊥ 8I+',2#85%'+ ! B  *BC mp SAB BC AH⊥ ⇒ ⊥  G<    *AH ABC⊂ #*   R  5P% ! '5I+/"%  52N4 ! 55%'+ !  AH SB⊥  .2NK%   *AH SBC⊥ AH SC ⇒ ⊥ * %D%  "'+ !  SK AK⊥ 5I+* 1  #*G%  *  *SC mp AHK⊥ Câu 1 7 : +<  &'+ ! -8$ '+ ! 9% ! N$D%  <  &G2 &/G%  '+ !  *SA mp ABCD⊥ #81 ! '9  :#3C9"4  ;* 1 ! &/;"&  *BD SAC⊥  #8%'+ ! B  *SA mp ABCD SA BD⊥ ⇒ ⊥ #* G<    *BD ABCD⊂     R  5  P% ! '  5I+  /"%   52N4 ! 5  5%  '+ !  AC BD⊥ 81 ! '9  $:#3C9"4  ;*+  "3UD,  & D1(  5  D%   5K2&/  9"4  ;    G%   3 '1 ! &/;"&  *IJ SAD⊥ G%  $D%  %"91(  &/'I ! +'2  %<  &G2 &/** 1  #*G%  *  *BD SAC⇒ ⊥ 8%'+ ! B  *SA mp ABCD SA DC⊥ ⇒ ⊥ G<    *DC ABCD⊂ #*    R  5  P% ! '  5I+  /"%   52N4 ! 5  5%  '+ !  CD AD⊥ $D%  <  &G2 &/** 1  #*G%  *  *CD SAD⇒ ⊥ %  UVVUD%  91(  &/5K2&/)<  &'2  %5%;/"% ! ' 4&  *IJ SAD⊥ Câu 1 8 :+51 ! 0"4  &$'+ ! 5%; /"% ! '$G2 &/',&5%  "$3'+ !  6A:67G%    *SA mp ABC⊥ #8 1 ! '9  :#3C9"4  ;* 1 ! &/;"&  *  *SAB SBC⊥ 8 1 ! '9  $:#3C9"4  ;* < ! &  3 **d A SBC #8%'+ ! B  *SA mp ABC SA BC⊥ ⇒ ⊥ G<    *BC ABC⊂ #*    R  5  P% ! '  5I+  /"%   52N4 ! 5  5%  '+ !  BC AB ⊥ 5%;/"% ! '$G2 &/5%  "$** 1  #*G%  *  *BC mp SAB⇒ ⊥  *  *SAB SBC⇒ ⊥ @<    *BC mp SAB⊂ 8K+&/5%;/"% ! '$3GI O 91(  &/'%+8 @<    *  *SAB SBC⊥  G%    *  *SAB SBC SB∩ = &4&   *AH SBC⊥ %N  3 **d A SBC 6 %'+ !     # # # AH AS AB = + %  67/V5*:  AC AB = 67  4&  # # #  #AH = + 7 # # A = = AAH⇒ = Câu 19: +W&G2 &/$8 3D,  &D1(  5DX5K2&/9"Y;'Z% $  G%   8  K4&  91[&/  5\&/  *d ABCD⊥ 5]"D^N ( ) S H≠ 8 #81 ! '  9   :  #3C  9"4  ;*_&/ ;"&K`&/B  *AC SHK⊥ 81 ! '  9   $:  #3C  9"4  ;*  a& P+b&/'c'5d9e&;-* )"e5']&W&G2 &/)`&/? #8%'+ ! B  *SH mp ABCD SH AC⊥ ⇒ ⊥ G<    *AC ABCD⊂ #* %D]"'+ !  AC BD ⊥ G%  $D%  %"91(  &/'I ! +'2  %<  &G2 &/* XVV$DX91[&/5K2&/)W&'Z%5%;/"c'$* 4& AC HK⊥ * 1  #*G%  *  *AC SHK⇒ ⊥ 8+"DX/"%+9"Y;'Z%GX35I+',2#5%'f  *AC SHK⊥ &4& DXP+b&/'c'5d9e&;-* %'f 7 ? CI CA= 7 8?  ? = 7 = Câu 20 :+W&'f-8$f 9cN$DXW&G2 &/']&% GX  *SA mp ABCD⊥ #81 ! '  9   :  3C  9"4  ;*  a& P+b&/'c'/"g%GX$)"e5 6% 8  1 ! '  9   :  3C  9"4  ;*a& P+b&/'c'5d9e&* #8%'+ ! B  *SA mp ABCD SA AB⊥ ⇒ ⊥ G<    *AB ABCD⊂ %D]"'f AB BC⊥ $DXW&G2 &/* 4&$DX91[&/G2 &//f''2&/'Z%GX$3.2NK%P+b&/'c' /"g%GX$DX$6% 8K+&/5%;/"c'Gh91[&/'%+ %'fB AH SD ⊥ i* j'Pc'5%'f AD DC⊥ $DXW&G2 &/*#* %D]"'f  *SA mp ABCD SA CD⊥ ⇒ ⊥ G<    *CD ABCD⊂ * 1  #*G%  *  *CD SAD⇒ ⊥ CD AH⇒ ⊥ ii* 1  i*G%  ii*  *AH SCD⇒ ⊥ @kNDXP+b&/'c'5d9e&;-* K+&/5%;/"c'G2 &/5%'fB    # # # AH AS AD = +   # # a a = +    # ? C  * ?a a a = + =  C C a AH⇒ = .    *CD ABCD⊂ * 1  #*G%  *  *CD SAD⇒ ⊥ CD AH⇒ ⊥ ii* 1  i*G%   ii*   *AH SCD⇒ ⊥ @kNDXP+b&/'c'5d9e&;-*. < ! 5&, ! 57&/"4  ;5K4&P+%  &/:* Câu 11: 1 ! &/;"&-1(&/5K<  & 7E 7 QAE  L#AEL76