đề toán thi thử năm 2015 số 15

 TRƯỜNG THPT NGÔ GIA TỰ  ! MÔN THI: TOÁN "#$%$&'()*+)$,-."/012"3'%240"#$%$&'."5067 Câu 1(2,0 điểm). "8")*9: ;  ; y x x= − +  < =C > a)"?8950@)@A6B0"C < =C DE&")*9:6FD"8> b) G$%$&86$4*DE&6B0"C < =C @)6H#'%0"I'% ;y x= − − () M 1@$J0."HK'%0LM'"0$J.0NOJ' @P$6B0"C < =C 0Q$6$4*M. Câu 2 (1,0 điểm). a) $?$."HK'%0LM'", 9$'  ; ; ;D89 R9$'x x x− = − b) M*9:."SD z 0"8?*F'6I'%0"SD ( )  ;zz z i+ − = Câu 3 (0,5 điểm). T'"%$50LC ( ) ( )  ;    (8% (8% (8% a b a a P a b b b −   = + +  ÷   <@P$  U  a b< ≠ < ≠ = Câu 4(1,0 điểm). $?$"V."HK'%0LM'", ( )   ;  ;  1   -  x y y x x y y x x  + + − = +  ∈  − − − + − =   ¡ Câu 5 (1,0 điểm)>T'"0TD"."W' ;  I x x dx= + ∫ Câu 6(1,0 điểm). "8"M'"D"X. >S ABCD DX65O ABCD ()"M'"D"Y'"Z01*[0+\' SAD ()0&*%$5D @N3'%0Q$ S 1"M'"D"$JN@N3'%%XDDE& S (\'*[0."I'%<ABCD=()6$4*H0"N]DDQ'"AD9&8D"8 ;HA HD = >G$M()0LN'%6$4*DE&AB>^$J0L_'% AD a = @)6H#'%0"I'%SC0Q8@P$65O*]0%XD  ; >T'"0"`8a0"40TD"2":$D"X.S.ABCD@)2"8?'%D5D"0a6$4*M6J'*[0."I'%<SBC=> Câu 7 (1,0 điểm). L8'%2"3'%%$&'@P$"V0G&6]Oxyz1D"86H#'%0"I'%   ,    x y z− − ∆ = = − 1*[0 ."I'%  < = ,    P x y z+ + − =  @)6$4*  ( ) ;UU A − >$J0."HK'%0LM'"6H#'%0"I'% d 6$bN& A Dc0 6H#'%0"I'% ∆ 0Q$B9&8D"82"8?'%D5D"0aB6J'*[0."I'% ( ) P +_'%> Câu 8 (1,0 điểm). L8'%*[0."I'%@P$"V0G&6] Oxy 1D"8"M'"@N3'% ABCD DX0W*I.LN'%6$4* DQ'"AB() <U;=M 10LN'%6$4*68Q'CI() <U=J >M*0G&6]D5D6d'"DE&"M'"@N3'%1+$J06d'"D 0"N]D6H#'%0"I'% ,  x y∆ − + = > Câu 9 (0,5 điểm). ]0"].D"S&  bN?DeN*)N6f1 ! bN?DeN*)Ng&'"@) h bN?DeN*)N@)'%>iO '%jN'"$\'Dk'%(/DL&  bN?DeN0a"].6X>T'"g5D9Ni09&8D"8  bN?DeN6HlD(iOL&DX6/'%*]0 bN?DeN*)N6f@)2"3'%bN5"&$bN?DeN*)N@)'%> Câu 10 (1,0 điểm). "8+&9:0"mDnHK'% 1 1a b c 0"f&*F'  Ra b ab c+ + + + = >"S'%*$'",     a b c a b c + + ≤ + + + Hết Thí sinh không được sử dụng tài liệu. Cán bộ coi thi không giải thích gì thêm. G@)0\'0"T9$'",oooooooooooooooo:+58n&'",ooooooooooo TRƯỜNG THPT NGÔ GIA TỰ ĐÁP ÁN I>LƯU Ý CHUNG, HP'%nj'D"i*D"d0LM'"+)O*]0D5D"%$?$@P$'"Y'%pDK+?'."?$DX>"$D"i*+)$"GD9$'"()* 0"`8D5D"2"5D'JN6/'%@)6Ep0"M@j'D"86$4*0:$6&> $4*08)'+)$0T'"6J'1!@)2"3'%()*0Lq'> P$+)$"M'""GD2"3'%%$&''JN0"T9$'"2"3'%@A"M'""8[D@A"M'"9&$0"M2"3'%D"86$4*0HK'% S'%@P$."e'6X> II. ĐÁP ÁN, Câu Ý Nội dung trình bày Điểm 1 a "8")*9: ;  ; y x x= − +  < =C > "?8950@)@A6B0"C < =C DE&")*9:6FD"8> 1,0 r=s, >D = ¡  r=m+$J'0"$\', $P$"Q', ($* U ($* x x y y →+∞ →−∞ = +∞ = −∞ &DX   t ; R > t   x y x x y x =  = − = ⇔  =  0,25 &DX t  < U= <U =1 t  <U=y x y x> ∀ ∈ −∞ ∪ +∞ < ∀ ∈ 9NOL&")*9:6B'%+$J'0L\' D5D2"8?'% < U=  <U =−∞ +∞ 1'%"CD"+$J'0L\'2"8?'% <U= > )*9:6Q0DmD6Q$0Q$ 1 <= x f= = U6Q0DmD0$4N0Q$ 1 <= x f= = − 0,25 ^?'%+$J'0"$\' 0,25 r=B0"C  4 2 -2 5 y x f x ( ) = x 3 -3 ⋅ x 2 ( ) +2 O 1 -1 2 0,25 b G$%$&86$4*DE&6B0"C < =C @)6H#'%0"I'% ;y x= − − () M 1@$J0."HK'%0LM'" 0$J.0NOJ'@P$6B0"C < =C 0Q$6$4*M. 1,0 G&6]DE&M()'%"$V*DE&"V ;  ;  ; y x x y x  = − +  = − −   0,25 ;  ; ; < U =  ; !  y x y x M x x x x = − − = − −   ⇔ ⇔ ⇒ − −   = − − + + =   0,25 "HK'%0LM'"0$J.0NOJ'@P$<C=0Q$M() t< =< = y f x= − + − 0,25 u< =  u h>y x y x⇔ = + − ⇔ = + 0,25 2 a $?$."HK'%0LM'", 9$'  ; ; ;D89 R9$'x x x− = − > 0,5 "HK'%0LM'"0HK'%6HK'% <9$'  R9$' = <; ; ; D89 = x x x+ − + = 0,25 9$' < 89 ;= ;<; D89 = x c x x⇔ + − + = <9$' ;=< 89 ;= x c x⇔ − + = 8 D89 ; 1 >x x+ > ∀ ∈¡ "HK'%0LM'"0HK'%6HK'% ; 9$' ;  9$'  x x− = ⇔ =  > ; < =  > ; x k k x k π π π π  = +  ⇔ ∈   = +   ¢ > ZO."HK'%0LM'"DX"&$"G'%"$V*, > ; x k π π = + U  > ; x k π π = + 1 < =k ∈¢ 0,25 b M*9:."SD z 0"8?*F'6I'%0"SD ( )  ;zz z i+ − = 0,5 ( ) ( ) ( )    ; ;  z x yi zz z i x y y x i= + ⇒ + − = ⇔ + − − + − = 0,25 ( ) ( ) ( )   ;  U U 1 U    x y y x y x  + − − = ⇔ ⇔ = −  − =  ,X"&$9:."SD0"8?*F'  z i = + @) z i = − 0,25 3 T'"%$50LC ( ) ( )  ;    (8% (8% (8% a b a a P a b b b −   = + +  ÷   <@P$  U  a b< ≠ < ≠ = 0,5 ( ) ( )     ;    (8% (8% (8% a a b a P a b b b −   = + +  ÷   ( ) ( )     (8% (8% ;(8%  a a b a a b b b −   = + +  ÷   0,25 ( )  ! (8% (8% R(8% a a b a a b b b   = + −  ÷    ! h (8% > R (8% R  a a a a b a b   = − = − =  ÷   0,25 4 $?$"V."HK'%0LM'", ( )   ;  ;  1   -  x y y x x y y x x  + + − = +  ∈  − − − + − =   ¡ 1,0 $7N2$V',    x y − ≤ ≤   ≥  > <= ( ) ( )  ;   ;  ;   u R x y x y x y x y y x⇔ + + = + + ⇔ + + = + + + + ( ) ( )     ;x y y x⇔ + − = ⇔ = + 0,25 "&O<;=)8<=0&6HlD,    - <=1<  g =x x x+ − − + − = ≤ ≤ <= ( ) ( )      u x x x⇔ + − + − − + − = ( )  ; ; u      x x x x x − − ⇔ + + − = + + − + 0,25 ( ) ; !    ; !     x y x x x = ⇒ =   ⇔  + = +  + + − +  0,25 sv0<!=>&DX, [ ]      ;   1  g U          x x x x  ≤  + +  ⇒ + ≤ ∀ ∈  + + − +  ≤  − +  [02"5D [ ] ; 1 g Ux + ≥ ∀ ∈ 0,25 ZO."HK'%0LM'"<!=@3'%"$V*> %"$V*DE&"V(), ( ) ( ) U ;U!x y = 5 T'"0TD"."W' ;  I x x dx= + ∫ 1,0 [0    t x x t dx tdt= + ⇔ = − ⇒ = 0,25 w$DZ'  U ; x t x t= ⇔ = = ⇔ = 0,25 ( ) ( )           I t t tdx t t dt⇒ = − = − ∫ ∫ 0,25  ! ;    R ! ; ! t t   − =  ÷   0,25 6 "8"M'"D"X. >S ABCD DX65O ABCD ()"M'"D"Y'"Z01*[0+\' SAD ()0&*%$5D @N3'%0Q$ S 1"M'"D"$JN@N3'%%XDDE& S (\'*[0."I'%<ABCD=()6$4*H0"N]D DQ'"AD9&8D"8 ;HA HD = >G$M()0LN'%6$4*DE&AB>^$J0L_'% AD a = @) 6H#'%0"I'%SC0Q8@P$65O*]0%XD  ; >T'"0"`8a0"40TD"2":$D"X.S.ABCD@) 2"8?'%D5D"0a6$4*M6J'*[0."I'%<SBC=> 1,0 M K D A B C H S H' 8HAx3HD@) AD a = ; UHA a HD a⇒ = = > L8'%0&*%$5D@N3'% SAD 0&DX  > ;SH HA HD SH a= ⇒ = 0,25 M ( ) SH ABCD⊥ '\' · ( ) ( ) ·  1 ; >SCH SC ABCD= =   >D80 ; ;HC SH a⇒ = =     >CD HC HD a⇒ = − = NOL&  > -  > ABCD S AD CD a= = 86X ; >  - R > > ; ; S ABCD ABCD a V SH S= = 0,25 MM()0LN'%6$4*DE&AB@)AHyy<SBC='\' ( ) ( ) ( ) ( ) ( ) ( )   1 1 1   d M SBC d A SBC d H SBC= = <= z HK BC⊥ 0Q$1 tHH SK⊥ 0Q$ tH > M ( ) ( ) t t < 1< == tBC SHK BC HH HH SBC d H SBC HH⊥ ⇒ ⊥ ⇒ ⊥ ⇒ = <= 0,25 L8'%0&*%$5D@N3'%SHK0&DX,           RR t t   a HH HH HK HS a = + = ⇒ = <;= a<=1<=1<;=0&6HlD ( ) ( ) RR 1 >  d M SBC a= 0,25 7 L8'%2"3'%%$&'@P$"V0G&6]Oxyz1D"86H#'%0"I'%   ,    x y z− − ∆ = = − 1*[0 ."I'% < = ,    P x y z+ + − = @)6$4* ( ) ;UU A − >$J0."HK'%0LM'"6H#'%0"I'%d 6$bN&ADc06H#'%0"I'% ∆ 0Q$B9&8D"82"8?'%D5D"0aB6J'*[0."I'% ( ) P +_'% 1,0 > 8 < U U =B B t t t∈∆ ⇒ + − U < =    < U< ==   u t t t d B P + + − + − = ⇔ =  0,25  ; t t =  ⇔  = −  0,25 P$  ( )  <UU= U U;t B AB= ⇒ ⇒ = − − uuur  10&DXn6$bN&<;UU =@)DX@0D.() ;    ,   ; x y z AB pt d − − + ⇒ = = − − uuur 0,25 P$ ( ) ; < U!U ;= !U;U t B AB= − ⇒ − − ⇒ = − − uuur 10&DXn6$bN&<;UU =@)DX@0D.() ; !  ,  ;  x t AB pt d y t z t = −   ⇒ = +   = − −  uuur  0,25 8 L8'%*[0."I'%@P$"V0G&6] Oxy 1D"8"M'"@N3'% ABCD DX0W*I.LN'%6$4* DQ'"AB()  <U;=M 10LN'%6$4*68Q'CI() <U=J >M*0G&6]D5D6d'"DE&"M'" @N3'%1+$J06d'"D0"N]D6H#'%0"I'% ,  x y∆ − + = > 1,0 H N M I D A B C J G$N()0LN'%6$4*CD@)H()0W*"M'"D"Y'"Z0AMND.G$<C=()6H#'%0Lq' '%8Q$0$J."M'"D"Y'"Z0AMND.a%$?0"$J019NOL&NJ//DI1n86XNJ@N3'%%XD@P$ AC1"&OJ 0"N]D<C=<@MAN()6H#'%2T'"DE&<C==>)MDD{'%()6H#'%2T'"DE& <C='\'JM@N3'%%XD@P$JD.<= 0,25 D0"N]D ∆ '\' < U = < U =1 < U;=>D t t JD t t JM+ ⇒ − + − uuur uuur "`8<= >   ; ;   < U =JD JM t t t D= ⇔ − + + + = ⇒ = − ⇒ − − uuur uuur > 0,25 G$a()DQ'""M'"@N3'%ABCD>|0"iO    !   a DM a a= = + ⇒ = > G$ < U =>A x y M     U ;  < ;=  R h  U < = < = R ! ! x y AM x y AD x y x y = − =   = + − =    ⇒ ⇔    = = = + + + =      P$ < U;= <U;= <U= <U = <U=A B I C J− ⇒ ⇒ ⇒ − ⇒ <0"f&*F'= 0,25 P$ ( ) R h R ; - u   U U U U ;U ! ! ! ! ! ! ! ! A B I C J − −         ⇒ − ⇒ ⇒ ⇒ −  ÷  ÷  ÷  ÷         <(8Q$=> ZO0G&6]D5D6d'""M'"@N3'%() < U;=1 <U;=1 <U =1 < U =>A B C D− − − − 0,25 9 ]0"].D"S&  bN?DeN*)N6f1 ! bN?DeN*)Ng&'"@) h bN?DeN*)N@)'%>iO '%jN'"$\'Dk'%(/DL&  bN?DeN0a"].6X>T'"g5D9Ni09&8D"8  bN?DeN6HlD (iOL&DX6/'%*]0bN?DeN*)N6f@)2"3'%bN5"&$bN?DeN*)N@)'%> 0,5 }=:."e'0~DE&2"3'%%$&'*jN()  R -CΩ = = }=G$ B ()+$J'D:•bN?(iO6HlDDX6/'%*]0bN?DeN*)N6f@)2"3'%bN5"&$ bN?*)N@)'%€>&gv0+&2"?'•'%9&N,  :D5D"(iObN?6f1;bN?g&'"(),  ;  ! C C  :D5D"(iObN?6f1bN?g&'"1bN?@)'%(),     ! h C C C  :D5D"(iObN?6f1bN?g&'"1bN?@)'%(),     ! h C C C 0,25 }="$6X  ;        !  h !  h ! h B C C C C C C C CΩ = + + = }=s5D9Ni0DE&+$J'D: B () ( ) h ;h - u B P B Ω = = = Ω 0,25 10 "8+&9:0"mDnHK'% 1 1a b c 0"f&*F'  Ra b ab c+ + + + = >"S'%*$'"     a b c a b c + + ≤ + + + 1,0 &DX ( ) ( )  R    -a b ab c a b c+ + + + = ⇔ + + + + = [0       x a a x y b b y z c c z = + = −     = + ⇔ = −     = + = −   @)2"$6X  R -a b ab c xy z+ + + + = ⇔ + = 0,25 ^DXnQ'%         x y z x y z x y z − − − + + ≤ ⇔ + + ≥ 0,25 "Z0@ZO0"`8^ 0&DX         x y x y z z xy xy + ≥ ⇒ + + ≥ + "`8^&ND"O D"‚&Lƒ0&DX    z xy xy z + ≥ + 0,25 ZO       x y z xy z + + ≥ = + iN•x€g?OL&2"$ ( ) ( ) U U ;U;Ua b c = 0,25 - Hết .  TRƯỜNG THPT NGÔ GIA TỰ  ! MÔN THI: TOÁN "#$%$&'()*+)$,-."/012"3'%240"#$%$&'."5067 Câu. = >"S'%*$'",     a b c a b c + + ≤ + + + Hết Thí sinh không được sử dụng tài liệu. Cán bộ coi thi không giải thích gì thêm. G@)0'0"T9$'",oooooooooooooooo:+58n&'",ooooooooooo TRƯỜNG