đề tự luyện THPT QG môn toán đề số 24

   Thời gian làm bài: 180 phút !"# ( ) 2 ( ) 2 x y x C x − = = + a)   ( )    y x∆ = + !"#$$%&'()*$+,-./$&( !"#$% 0 1$$)234: $  5 6  $7x c x + = +  )8! z 90:$;<=$+    > i z i+ − − = ,4)?!@0)8! w zi z= − +  !"&#$ 'A. 1$$B)234 > > C   C   x x− + − ≤ !"$  1$$+)234: >       5      >  y y x y xy x y x y x x  + + − − =   + + + = − −   !"#$,-/$+-!4)$D$#E$   x y x + = − !!3F!G0. !"'$4!H)I&(J!HK&(JC40D$KCDC&JL!! I&'&JM$.<MH!D$0<LI&N&NJN a 2 &JN(,-%-!!@0 =$!H)I&(J=!!$O00$I(J !"($,3P)D$+G0.Q7K'!0$!&(/ D$(!"!!!#&('&C?CR#$ST0! = AM CN ($U3VSW5L 'AL!* )*$!3!@0H!&CJ LWX:K4G0.!@0&( !")#$,3=M$0D$+G0.Oxyz'!0$   >   >  x y z− − ∆ = = −    >   Y 5 A x y z− − ∆ = = − ,4G0.$0$%!@0  ∆   ∆ $U)234P)Z0!   ∆ C4!$U<<MH!!@0  ∆ C[P)Z !"*#$ 'A Một HYG!$!H[=!0<'3H!H0$G!$[C&(4 \U)]<$[HG!$H./G!,-7!<B0!0$G!$& (48!#0< !"$ x'yC0$^!90:$;<=$+ 5 > ≥++ xyyx ,4$39B!@0$U< 8!  A5>>  +−−+−+= xyxyyxyxP  __________XU__________  XG[-$____________I/0_________ O=`$__________O=`$_________ +,-./0123  !" $m $$4 $$5 #,a)7! bc dD = −¡ e ( )  5 f '  y x D x − = < ∀ ∈ + e,$+!a0KNW4 C$ L C$  x x y y →−∞ →+∞ = − = − e,$+!a87NW4 ( ) ( )   C$ L C$ x x y y − + → − → − = −∞ = +∞ e($U$[ 6  ∞ 7 8 ∞ 9  7 7  7 7 ∞ 8 ∞ 7 X!$U3[W ∞ LW'WLg ∞  X=M!H!^!3 e$%P!$+ : ' 7 7     7& ;:.   e x y y=-1 x=-2 0 -2 1 2 -1 -3 -5 3 e1G$ ( ) LM x y C$U)$% e  f  5 >L ff   5f x x x f x x= − + = − e ff   5 f x x x= ⇔ − = ⇔ = eI<K30' ( )   > y f= = ' f  f f x f= = − eZ234$U)<KU ( ) ( ) fy f x x x y= − + 'A 'A 'A 'A 'A 'A  ( )  6   > > x x= − − + = − + ehaK)234$U)<KU!?4C 6 > y x= − + 'A 'A $$4 <=<>1+?-@AB1 $  5 6  $7x c x + = + ($Ui$)234;/# $7 5   $7j5!   !  vn x x =   − = ⇔  =  hD$  !7   > x k π π = ⇔ = ± + C)234!HG$+  ' > x k π π = ± + 0,25 0,25 $$5     )8!  z  90  :  $;<  =$+     > i z i+ − − =   ,4  )?    !@0    )8! w zi z= − + 1$k  ' z x yi x y z x yi= + ∈ ⇒ = −¡  ,l$$U'0!H      >    >  x i x yi i x y x y i y =  + − − − = = ⇔ + − + − − = ⇔  = −  I<K30 z i = −  ,0!H      >  w i i i i i i i= − − + + = + − + = − haK m w = − 0,25 0,25 $&  x > (Z,   > > C   C   x x⇔ − + − ≤ > > > C   C    C    x x x x⇔ − + − ≤ ⇔ − − ≤     >  >  x x x x− − ≤ ⇔ − − ≤    x⇔ − ≤ ≤ UR)0!Ha)$+C ( ] LS = 0,25 0,25 $ <=<1C>1+?-@AB1 >       5       >   y y x y xy x y x y x x  + + − − =   + + + = − −   ($Ui$)0?<;/#         y y y y x y y x =   − + + − = ⇔ = −   = −  ,XhD$KN0K)  6 > Y x x+ + = M$+ ,XhD$KNj0K > Y x x + = ⇒ = − <K30$+7LKNjLj 0,25 0,25 0,25 0,25 ,X>hD$ y x= − 0K 5      A >          x x x x vn+ + = ⇔ − + + + = C+)234!H$+  L   L x y = − − $ D1.<C@D011B1>1E--<,<1F5G<HI@1J1K3LM   x y x + = − NK0O0@AP0@Q4HR !"3F!#$jL JH    x S dx x − + = − ∫ ,0!H    x S dx x − + = − ∫ N  >    dx x − + − ∫   >C   n x x − = + −  >  >C >C  >  = + = − 0,25 0,25 0,25 0,25 $' 1S1B101T>U$VW0THOXVWYK1B1@14-N,<HOXY,YKWZ0O0H+[- @1E-U\NKWH<3R@N"--T0N,<14"ZU]]W] a 2 NKW]V$ D1@1^@D010_4;1M<01T>U$VWNK;1S=-0O01-<`414<H+[-@1E-UVNKW$ ,0!HI&⊥&I&⊥J ⇒I&⊥&(J ∆&J<M!*#$ ⇒&JN0⇒(N0 1G$mC3<$%&J⇒&mN('&moo(m⊥ &J⇒&(mC4<M ⇒&(⊥&J JHI &(J N 2 (AD BC).AB 3a 2 2 + = haKh I&(J N 2 3 ABCD 1 1 3a a 2 .S .SA . .a 2 3 3 2 2 = =  ,0!HJoo(m⇒JooI(m⇒/I('JN/J'I(mN/'I(m 1G$XN&∩(m&⊥IX#$,0!H&⊥I(m⇒/&'I(mN& 0,5 0,5 ,0!H 2 2 2 2 2 2 1 1 1 1 4 5 AK SA AH 2a 2a 2a = + = + = ⇒&N a 10 5  ⇒/&LI(mN&N a 10 5 h4XC3<$%&[/LI(mN/&LI(mN a 10 5 haK/J'I(N a 10 5   !" ( AS-3a@>1E-N,<1C@Q4HR:X\01S@43-<O0V$+[-@1E-.LS-LS-N,< V0b@0O00F1V\YcY+d@@F<NKL4S01S = AM CN $V<e@Af-%7Zg\ %ZgNK01!H+[->1!-<O0@AS-0_4-T0YKW%Z7g$hX@B3@Q4HR0_4NK V 1G$JfC$%3[!#(0!JfNST ,0!HSTJfC44 ⇒SJfNTN&S⇒∆&SJf!*#$S ⇒∠SJf&N∠S&JfNJf& ⇒&JfC)*$!!@0H!&⇒Jf3pJ&q<0 SJ ⇒&!Hl!2!r)2C MD uuuur N5LW ⇒& x 5 4t y 2 t  = +  = −   &∈&⇒&Ag50LW0⇒ MA uuuur Nsg50LW0 ,0!HS&NSJ⇔sg50  gW0  N⇔0  gY60g6AWN ⇔0NWhaK %7&Zg$ MA uuuur NL5⇒&( x 4 y 1 4 + = ⇔57WKNWYL DC uuur NAL>⇒( x y 1 5 3 + = ⇔>7W AKNA JH( 4x y 16 3x 5y 5  − = −  − =  ⇔ x 5 y 4  = −  = −  haK(WALW5 'A 'A $) AS-;1--<4N,<1C@Q4HROxyz\01S14<H+[-@1E-   >   >  x y z− − ∆ = = − NK  >   Y 5 A x y z− − ∆ = = − $B3@Q4HR-<4SH<^30_4  ∆ NK  ∆ NKN<e@>1+?-@AB13a@ >1E-%gL4S01SH+[-@1E-  ∆ YK1B101<e"N"--T00_4H+[-@1E-  ∆ Yi 3a@>1E-%g$ $* h$UC#$  ∆   ∆ /D$/#0 1$$+)2344R!$0$%&>L L   ∆ !Hh,Z ( )  L >Lu = − ur   ∆ !Hh,Z ( )  YL5L Au = − uur 1G$tCP)!80   '∆ ∆ 4t!Hh,Z,C   ' LLYn u u   = =   r ur uur h4  ∆ C4!$U<<MH!!@0  ∆ C[P)Z ⇒ Z!80  ∆     P Q⊥ JHZ!u$q<0&!Hh,Z,C   '  5LsL  5n n u   = = − −   ur uur uur Z!H)234C 5 s  5 6A x y z− + − + = R@1T3-I3'1Q0L<10T@i;1O014"\@AS-HT0T14<1Q0L<1@iYKNK VB1$6e>-/"1<i1T31Q0L<1HT@1K13R@1K-.Q0$D1:O0L"2@L4S01S 14<1Q0L<1NKVB1Hj-0F114" Sv$!!7U)]<$[YG!$/G!C.!@0Y)? tử   Yw  n⇒ Ω = = )?k 1G$&C$U!x&(48!#0<x    Aww 5 n A⇒ = = )?k    5       > n A P A n ⇒ = = = Ω )?k 'A 'A 'A 'A 'A 'A $ 1Sx\yYK14<LM@1k0@1l43hH<m";<C 5 > ≥++ xyyx $B33<0_45<e"@1j0  A5>>  +−−+−+= xyxyyxyxP $ hD$G$^!7'K0C<M!H xyyx 5  ≥+ '[y$;<=$+<K30 >  > >        5       x y x y x y xy x y x y x y+ + + ≥ + + ≥ ⇒ + + + − ≥ ⇒ + ≥ ,0$Ui$Z 0<  A5>  >   >  +−−++−+++= xyxyxyyxyxyxP   A  >   > 55 ++−+++= yxyxyx > J    55 yx yx + ≥+ [y><K30  A 5 s  ++−+≥ yxyxP P tyx =+  4   ≥t / ≥+ yx  0,25 0,25 0,25 \z  A 5 s   +−= tttf D$   ≥t '!H   s f >−= ttf 'D$   ≥t [ {$U3[       +∞L   I<K30 Y >>>   $ L   =       =       +∞∈ ftf t  JH1,TT!@0ZV Y >>> '#R!=$!r=$   == yx 0,25