!"#$%&'(')*+,)-'.)-'/ +012 34565' Thời gian làm bài: 150 phút (không kể thời gian giao đề) 78'9)6/điểm: x y x + = − ( ) C !"# m $%&"'" ( ) ( d y x m= − ) ( ) C *$+, - .A B /012 ( ) C 78)9'6/điểm:3+%4"#!( ( ) 5 6 5 sin x cos x cos x + = − ÷ π 78;9'6-điểm:%&"'" d ,d ""72 #%&"'" d 89$ +,-.#%&"'" d 8 n $+,- ( ) n ,n∈Ν ≥ :5$1;"'" "#"$8#<=+>"?#/"8699"%@<=+ A%=B ! n C 78.9'6-điểm: !<D"#E" ABC.A' B' C' 8B<"02* a .**7B >"8/" 9 F9 3G M <#2"$* BC I <#2"$ AM ?#/" !2$ I <HB A' B' C' <#G", G A' B' C'∆ I$I1<D"#E ABC.A' B' C' 78/9'6-điểm: !$J+%4"#!28"- ∈ + x 0;1 3 ( ) 9m x x x( x )− + + + − ≤ 78<9'6-điểm: ABC∆ 8#2"$* BC < ( ) 5 M ;− .%&"'":%&"1KL B M2$ ( ) 5E ;− − %&"'": AC M2$ ( ) 5F ; N$O:"P A M2,%&"#Q"*+ ABC∆ <$ ( ) R D ;− !*>P ABC∆ 78=9'6-điểm:3-+%4"#!( 5 5 5 5 5 6 x x y y x y y − + = + − = + 78>9'6-điểm: !"#SJ( − + − + = − + x x x x f x x x 4 3 2 2 4 8 8 5 ( ) 2 2 TTTTTTTTTT?TTTTTTTTTT Thí sinh không được sử dụng tài liệu. Cán bộ coi thi không giải thích gì thêm. UGI(VVVVVVVVVVVVVVWXY(VVVVVVV !"#$%&'(')*+,)-'.)-'/ +012 34565'6 Thời gian làm bài: 150 phút (không kể thời gian giao đề) (@$+A (Văn bản này gồm 06 trang) A:BCDEF8D1 Z2I<không theo cách nêu trong đáp án nhưng vẫn đúng!$ L"+[%"$M2B \-"$]28#"%7"Y^J+1;"<<- %7"Y^J+%@"J-#""J 5N$I-)/$]21>"$."_"2B1M2 AA:2G2HIJDK4L1 78 2G2 4L 78' 9)6/ K4L: IM3 x y x + = − : NM2JMOP4QJ4RHIHSKTJU ( ) C VIM3KW =+O( { } D \= ¡ 8( ( ) 5 9 y' x − = < − x D∀ ∈ U"#1" ( ) ;−∞ ( ) ;+∞ U1;"8# -)/ -)/ I x x lim y lim y →−∞ →+∞ = = =%&"'" y = <%&"- ="" I x x lim y ;lim y ; − + → → = −∞ = +∞ =%&"'" x = < %&"-=:" -)/ ?"( x ∞'X∞ y’ y )X∞ ∞) -)/ N( -)/ P:Y2D42JZUV m KLKB[DJ\D ( ) ( d y x m= − ]JKTJU ( ) C J^44K4L G7P4_J .A B `Ha42b28V ( ) C `a+%4"#!>"$ ( ) ( d y x m= − ( ) C ( ( ) x x m x + = − − \7G x ≠ .+%4"#! ( ) ( ) ( ) R 9 x m x m⇔ − + + − = N$ ( ) ( d y x m= − ) ( ) C *$+,- .A B /0 12 ( ) C !+%4"#!]+8"-+,- x ,x x x< < -)/ -)/ NH ( ) R f ( x ) x m x m= − + + − b2[2 9. f ( )⇔ < -)/ ?c 9 9 R 9.f ( ) f ( ) . ( m ) m< ⇔ < ⇔ − + + − < 5 9 m⇔ − < ⇔ ∈¡ -)/ QJc8d1C4e4D42JZUJOVmKa8JfWgR8h8VPI4J2 -)/ 78) 9'6/ K4L: 4N4GBiDJZY1 ( ) 5 6 5 sin x cos x cos x + = − ÷ π 8( ( ) ( ) 5 6 5 6 5 sin x cos x cos x sin x sin xcos x sin x π π + = − ⇔ + = − − ÷ -/ ( ) R 5 5 R sin x sin x=-sin x sin x+sin x sin x=0⇔ + ⇔ + -)/ R sin xcos x sin x=0⇔ + ( ) sin x cos x =0⇔ + ( ) ( ) 9 9 sin x cos x = ⇔ + = -)/ 3] k x ;k π = ∈¢ WQ];"- -)/ QJc8dGBiDJZYjD4_1 k x ;k π = ∈¢ -)/ 78; 9'K4L: 4KB[DJ\D d ,d MDMDHC48ZRKB[DJ\D d j'-K4L G7P4_J6JZRKB[DJ\D d j n K4LG7P4_J ( ) n ,n∈Ν ≥ k;K4LblD J\DIDJZDM32K4Lj4JZRcdGJImJJD42n4QJZ`Dj)> J D42KBocdGJp2BHdgY n q X"8P2> d .P2> d <( 9 n C .C -)/ X"8P2> d .P2> d <( 9 n C .C -)/ A"( 9 n C .C d 9 n C .C e699 ( ) ( ) 9 9 699 6 n! ! n! . . n !. ! !. ! n ! ⇔ + = − − -)/ 6 fF9 9n n⇔ + − = 9 6 n n = ⇔ = − QJc8d1 9n = -)/ 78. 9'K4L: YcrDJZsJD42 ABC.A' B' C' jK2gcIJD42Ka8^ a 6^PRJ^ HC4K2gmJDjP`D 9 F9 e4 M cIJZ8DK4L^ BC HI I cIJZ8DK4LV AM n4QJZ`DY4Q8VK4L I cRtJK2g A' B' C' cIJZeDJ7 G V A' B' C'∆ uJLJub34crDJZs ABC.A' B' C' U!( 3G M ' <#2"$ B' C' W K A' M '∈ A' K KG GM '= = K AH A' M';H A' M '⊥ ∈ -)/ 8 AHGI <!! IG AH= U4_ AM A' M' = . I <#2"$ AM . G <#G", A' B' C'∆ H<#2"$ A' K F A' H A' M '⇒ = -)/ 8( 5 R a dtA' B' C' = W 5 a A' M' = 5 a A' H⇒ = 9 5 F9 5 R a a AH A' H .tan .= = = -)/ vKj1 5 5 5 R R F ABC .A' B'C' a a a V AH.dtA' B' C' .= = = (đvtt) -)/ 78/ 9'K4L: YKLPwJGBiDJZYM8jD4_ ∈ + x 0;1 3 1 ( ) 9m x x x( x )− + + + − ≤ NH 2 t x 2x 2= − + ∈ +dox [0;1 3] [ ] Wt ∈ -)/ ?J+%4"#!%4"%4"7( − ≤ + 2 t 2 m t 1 -)/ t g(t) t − = + 2 2 1 7 [ ] Wt ∈ 8( + + = > + 2 2 2 2 0 1 t t g'(t) (t ) \=B t g(t) t − = + 2 2 1 "# [ ] ; \Y8( ] ] 5 Maxg t g = = -)/ L8( 2 t 2 m t 1 − ≤ + 8"-∈g.h ⇔ [ ] t m g t g 1;2 2 max ( ) (2) 3 ∈ ≤ = = <2=( 5 m ≤ -)/ 78< 9'K4L: ABC∆ jJZ8DK4L^ BC cI ( ) 5 M ;− 6KB[DJ\DkKB[Dbx Jv B K4y8K4L ( ) 5E ;− − HIKB[DJ\Dk AC K4y8K4L ( ) 5F ; 4L K34zkDVK{ A y8J7KB[DJZ|D^4J4QG ABC∆ cIK4L ( ) R D ;− YJ^Km2K{V ABC∆ U!( -)/ 3G H <#, ABC∆ !8 BHCD <!!.M<#2"$ HD ( ) 9H ;⇒ BH : ( ) 5E ;− − ( ) ( ) 9 9 5 9 x y BH : BH : x y − − = ⇔ − − = − − − − i DC BHP ( ) R D ;− 2>DC ( ) F 9DC : x y− − = i BH AC⊥ ( ) 5F ; 2>j ( ) R 9AC : x y+ − = -)/ i C AC DC= ∩ G><"-- F 9 R 9 x y x y − − = + − = !%@ ( ) f C ;− ( ) 5 M ;− <#2"$ BC ( ) B ;− ( ) R 9BC ;⇒ = uuur -)/ i H <#, ABC∆ AH BC⊥ ( ) 9AH : x⇒ − = i A AH AC= ∩ G>j<"-- 9 R 9 x x y − = + − = ( ) A ;⇒ QJc8d1 ( ) A ; W ( ) B ;− W ( ) f C ;− -)/ 78= 9'K4L: 4N4_GBiDJZY1 5 5 5 5 5 6 x x y y x y y − + = + − = + N021-( 5 5 9 6 9 9 9 y y x y y y x + ≥ ≥ + ≥ ⇔ ≥ − ≥ -)/ 8( -)/ ( ) ( ) ( ) 5 5 5 5 5 5 5 5 5 5x x y y x x y y− + = + ⇔ − − − = + − + ( ) ( ) 5f x f y⇔ − = + 7 5 ] 5f t t t= − `a 5 ] 5f t t t= − 7 [ ) Wt ∈ +∞ 8 ( ) k] 5 5 5 9f t t t= − = − ≥ U 5 ] 5f t t t= − "# [ ) W+∞ ZL ( ) ( ) 5 5 5 f x f y x y x y− = + ⇒ − = + ⇔ − = + − -)/ L 5 6x y y− = + ⇒ ( ) l 6x y y− = + ( ) l 5 6y y y⇔ + − = + l 5 6 ly y y⇔ + = + + Với điều kiện 9y ≥ .!+%4"+%4"#!#c( R 5 F m F5 F 9y y y y+ + + − = ( ) ( ) 5 m ll F 9y y y y⇔ − + + + = X2B# y = 5x = <2=(U-8"-Y2BJ( 5 x y = = -)/ 78> 9'K4L: YD42JZUfwJVIM31 − + − + = − + x x x x f x x x 4 3 2 2 4 8 8 5 ( ) 2 2 =+O( D = ¡ -)/ 8( = − + + − + f x x x x x 2 2 1 ( ) 2 2 2 2 WP#( ( ) − + = − + ≥ x x x 2 2 2 2 1 1 1 -)/ A?N 2B( f x x x x x 2 2 1 ( ) 2 2 2 2 2 = − + + ≥ − + -)/ N'":OB# ⇔ + = ⇔ = x x x 2 –2 2 1 1 dg1 Minf( x ) = K^JKBob4 x = -)/ TTTTTTTTTTTTTTTTTTTTTTTUTTTTTTTTTTTTTTTTTTTTTT . = <2=(U-8"-Y2BJ( 5 x y = = -)/ 78> 9'K4L: YD42JZUfwJVIM 31 − + − + = − + x x x x f x x x 4 3 2 2 4 8 8 5 ( ) 2 2 =+O( D = ¡ -)/ 8( = − + + − + f x x x x x 2 2 1 ( ) 2 2 2 2 WP#( ( ) − + = − + ≥ x x x 2 2 2 2 1 1 1 -)/ . [0 ;1 3] [ ] Wt ∈ -)/ ?J+%4"#!%4"%4"7( − ≤ + 2 t 2 m t 1 -)/ t g(t) t − = + 2 2 1 7 [ ] Wt ∈ 8( + + = > + 2 2 2 2 0 1 t. 2 1 1 1 -)/ A?N 2B( f x x x x x 2 2 1 ( ) 2 2 2 2 2 = − + + ≥ − + -)/ N'":OB# ⇔ + = ⇔ = x x x 2 –2 2 1 1 dg1 Minf( x ) = K^JKBob4 x = -)/ TTTTTTTTTTTTTTTTTTTTTTTUTTTTTTTTTTTTTTTTTTTTTT