KTCL 8T HK II THPT TRUC NINH B

 TRƯỜNG THPT TRC NINH B  ! HƯỚNG DẪN CHẤM & BIỂU ĐIỂM MÔN : TOÁN LỚP 12 ( Hướng dẫn chấm này c 02 trang ) Lưu ý: • Làm tròn điểm theo quy tắc: "#$ "#$% "#$ "#$% "#&$ $#→ → → . • HS trình bày lời giải khác cách của đáp án, nếu đúng thì cho điểm tương đương. - Bi 1(3.50 điểm): '(')*+, "   /  !y x m x m=− + + − + 01234'5 - / m C 6*7)4'8*+,# !9':(+;4<)<=234'5  - /C %9>**2?234'5 - / m C 01@82A?*0B04C5D'EF@AG44H(4')F'*I448*JA;02KL# Bài 1 Nội dung Điểm số 1/ (2.50 điểm) M'A*N601'+ "    & - /y x x C= − + − %MOPN 0.25 M1 7A* x y →−∞ = −∞ % 7A* x y →+∞ = −∞ 0.25 M1 . Q " !Ry x x= − + S;025F'4CTF% Q  % y x x = ⇔ = = ± 0.25 MUUP 0.50 M+U4CTF*VAW'(:FJ ( ) %− <) ( ) %+∞ %+U4CTFW'(:FJ ( ) % −∞ − <) ( ) % # 0.25 M+2H40B04A?L4HA2A?*  & CT x y= ⇒ = − %+2H40B02H44HA2A?*  CT x y= ± ⇒ = # 0.25 M34'5PX/1  Y ! !Ry x= − + S;025F'4CTF% !6  . Y  . y x ± = ⇔ = % Yy 2ZA[\LW'A x ]L82A?**VA2A?* !6 x # TF !   . !&  . !& - % /6 - % / . . U U− 7)'8A2A?*L,F0^8  - /C # 0.25  { }   / - / -% &/% / - / - &%/% - !%/% -!%/% - &%/ C Oy O C Ox A B C D + ∩ = − + ∩ = − −  0.50 2/ (1.00 điểm) M1 .   .  Q "  /  - . /% Q  %  m y x m x x x m y x x + = − + + = − − − = ⇔ = =  0.25 M - / m C 01@82A?*0B04C5D'EF@AG4W'A<)0'_W'A Qy 01.FJ'AG*D'EF@AG4 .     . m m + − ⇔ > ⇔ > -M/ M'A21 Qy 01.FJ'AG*D'EF@AG47)P !  . ! .  .     m m x x x x + + = − < = < = − = #`A.2A?*0B04C5D'EF@AG40^8 - / m C 7) ! !   . . - % /6 - % /6 - % /A x y B x y C x y %4C(FJ21 "    ! . ! !  /  !6  !y y x m x m y m= = − + + − + = − + # 0.25 M(4aF'0'\4234'5')*+,4CbFJD'cdFJ6+LeC8 ABC∆ 0EF4HA2_F' B #fge ABC∆ 2KLW'A<)0'_W'A AB AC= # 0.25 M1      !  ! . ! . ! - / - / - / - /AB AC x x y y x x y y= ⇔ − + − = − + −   "    ! ! ! ! h / i "x x m x x⇔ + − + = .    ! !   . h /i . ### . x x m m − + ⇔ − + = ⇔ ⇔ = -4'j8*kF-M// 0.25       !!x  &  y     XX & −∞ −∞ Trang 1/2 Bi 2(1.00 điểm): A:AD'cdFJ4C>F'P " R#   x x − + = # Bài 2 Nội dung Điểm số (1.00 điểm) Ml   R#    % " x x x x ⇔ − + = ⇔ = = 0.50 M1   ! ! x x x= ⇔ = ⇔ = ± #M1   "     x x x x= ⇔ = ⇔ = ⇔ = ± # 0.50 Bi 3(2.00 điểm): !9>**I4FJLeTF')* - /F x 0^8')*+, - / - !/+AF f x x x= − 6@Am4 - / ! " F π = %9aF'P  ! !  ! x x dx e e − − − − ∫ # Bài 3 Nội dung Điểm số 1/ (1.00 điểm) Mn4   ! ! +AF  0(+  du dx u x dv xdx v x =  = −   ⇒   = = −     ! - / - !/0(+ 0(+  F x x x xdx⇒ = − − + ∫ 0.50 ! ! - / - !/0(+ +AF    F x x x x C⇒ = − − + + 0.25 M1 - / ! " F π =  ! ! ! - !/0(+ +AF !       C C π π π ⇒ − − + + = ⇒ = #fge ! ! ! - / - !/0(+ +AF     F x x x x= − − + + 0.25 2/ (1.00 điểm) Mn4 ! 6 - !/ 6 -/ ! x x t e dt e dx t e t − = ⇒ = − = = #(21 !  !  ! ! !  !  x x e I dx dt e e t t − − − = = − − − − ∫ ∫  0.25 ! ! ! ! ! ! ! ! - / - !/ ! ! ! h i - !/- / . - !/- / . - !/  e e e t t I dt dt dt t t t t t t − − − − − + ⇒ = = − = − − + − + − + − ∫ ∫ ∫ 0.25 ! ! ! ! ! ! ! - !/ ! - / ! -7F ! 7F  / . - !/ .  . e e e d t d t I t t t t − − − + − ⇒ = − + = − + − − + − ∫ ∫ 0.25 ! ! ! ! ! ! ! ! ! ! ! ! ! - / 7F h7F 7F i 7F # .  . !  . ! e t e e I t e e − − − − − + + + − = − = − − = − − − − + 0.25 Bi 4(3.50 điểm):C(FJW'oFJJA8F<pA'G4`82I Oxyz 60'('>F'0'1D #S OABC 012;e7)'>F'<LoFJ OABC <pA -%%/6O -%%/6A -%%/6C  -%%/S #`A 6M N 4'q(4'r4B7)4CLFJ2A?*0;00HF' 6SA SC % P 7)'>F'0'AmL<LoFJJ100^8 O 4CTF SB # !9fAm4D'cdFJ4C>F'*n4D'sFJ - /OMN %9>*4`82I0^82A?* B 6<q04d SB uuur #'rFJ*AF' P 4'LI0*n4D'sFJ - /OMN # .9aF' #OM MB uuuur uuuur #'rFJ*AF'&2A?* 6 6 6 6 6 6O A B C M P N 0bFJ4'LI0*I4*n40tL#fAm4D'cdFJ4C>F'*n40tL21# "9aF'4'?4a0'0^8W',A4CuFS(8e+AF'@vAW'A]L8e48*JA;0 SOB -W?0:0;02A?*4C(FJ/]L8F'2cwFJ4'sFJ SB # Bài 4 Nội dung Điểm số 1/ (1.00 điểm) Mx2K@)A6+LeC8 -!%%!/6 -%!%!/M N 0.25  -!%%!/6 -%!%!/ h 6 i - !% !%!/ OM ON n OM ON⇒ ⇒ = = − − ≠ uuuur uuuur uur uuuur uuuur ur 7)*I4<q04dD';D4LemF0^8 - /OMN 0.25  - /OMN⇒ 01D'cdFJ4C>F'P !#- / !#- / !#- /  x y z x y z− − − − + − = ⇔ + − = 0.50 2/ ( 0.75 điểm) M801 -%%/ -%%/OB OA OC B= + = ⇒ uuur uuur uuuur  -%% /SB⇒ − uuur 0.50  SB n SB⇒ = − ⇒ uuur ur uuur 7)*I4<q04dD';D4LemF0^8 - /OMN  - /SB OMN⇒ ⊥ M1 - / - / - / - / SB OMN OP SB OP OMN P OMN O OP OMN ⊥   ⊥ ⇒ ⊂ ⇒ ∈   ∈ ∩  0.25 3/ (0.75 điểm) M1 # ### OM MB = = uuuur uuuur 0.25 OM MB⇒ ⊥ #cdFJ4B01 ON NB⊥ #1 6 6OP PB OA AB OC CB⊥ ⊥ ⊥ 'rFJ4j&2A?* 6 6 6 6 6 6O A B C M P N 0bFJ4'LI0*I4*n40tL2cwFJWaF' OB 0.25 M#021014E* -!%!%/I 7)4C92A?*2(HF OB <)@9W !   R OB= = #fge*90tL01D94C>F'P    - !/ - !/ - / x y z− + − + − = 0.25 4/ (1.00 điểm) M`A - /H 7)W',A4CuFS(8e+AF'@vAW'A]L8e48*JA;0 SOB -W?0:0;02A?*4C(FJ/]L8F'2cwFJ4'sFJ SB # M1 # ### OS OB = = uuur uuur OS OB⇒ ⊥ SOB⇒ ∆ <LoFJ4HA O <)012cwFJ08( OP 6 P vJAy8<)U# 0.25 M'A]L8e0;0*AKF 6SOP BOP∆ ∆ ]L8F'294'sFJ SB 7tF7cz44H(4')F''8AW',AF1F ! - /H 6  - /H  !  - / - / - /H H H V V V⇒ = + 0.25 M801   - / ! ! # # . . H V OP SP OP BP π π = +   ! ! #- / # . . OP SP BP OP SB π π = + = 0.25 M1     ! ! !  . OP OP OS OB = + ⇒ = %    .SB OS OB= + = - / !  !R . # # . # . . H V π π ⇒ = = 0.25  l    {   U Trang 2/2 . OM MB = = uuuur uuuur 0.25 OM MB⇒ ⊥ #cdFJ 4B 01 ON NB⊥ #1 6 6OP PB OA AB OC CB⊥ ⊥ ⊥ 'rFJ4j&2A?* 6 6 6 6 6 6O A B C M P N 0bFJ4'LI0*I4*n40tL2cwFJWaF' OB 0.25 M#021014E* -!%!%/I 7)4C92A?*2(HF OB <)@9W !   R. -%%/OB OA OC B= + = ⇒ uuur uuur uuuur  -%% /SB⇒ − uuur 0.50  SB n SB⇒ = − ⇒ uuur ur uuur 7)*I4<q04dD';D4LemF0^8 - /OMN  - /SB OMN⇒ ⊥ M1 - / - / - / - / SB OMN OP SB OP. + # 0.25 M(4aF'0'4234'5')*+,4CbFJD'cdFJ6+LeC8 ABC∆ 0EF4HA2_F' B #fge ABC∆ 2KLW'A<)0'_W'A AB AC= # 0.25 M1      !  ! . ! . ! - / - / - / - /AB AC x x y y x