TRƯỜNG THPT NGÔ GIA TỰ ! MÔN THI: TOÁN "#$%$&'()*+)$,-."/012"3'%240"#$%$&'."5067 Câu 1(2,0 điểm). "8")*9: ; ; y x x= − + < =C > a)"?8950@)@A6B0"C < =C DE&")*9:6FD"8> b) G$%$&86$4*DE&6B0"C < =C @)6H#'%0"I'% ;y x= − − () M 1@$J0."HK'%0LM'"0$J.0NOJ' @P$6B0"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'"%$50LC ( ) ( ) ; (8% (8% (8% a b a a P a b b b − = + + ÷ <@P$ 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 DX65O ABCD ()"M'"D"Y'"Z01*[0+\' SAD ()0&*%$5D @N3'%0Q$ S 1"M'"D"$JN@N3'%%XDDE& S (\'*[0."I'%<ABCD=()6$4*H0"N]DDQ'"AD9&8D"8 ;HA HD = >G$M()0LN'%6$4*DE&AB>^$J0L_'% AD a = @)6H#'%0"I'%SC0Q8@P$65O*]0%XD ; >T'"0"`8a0"40TD"2":$D"X.S.ABCD@)2"8?'%D5D"0a6$4*M6J'*[0."I'%<SBC=> Câu 7 (1,0 điểm). L8'%2"3'%%$&'@P$"V0G&6]Oxyz1D"86H#'%0"I'% , x y z− − ∆ = = − 1*[0 ."I'% < = , P x y z+ + − = @)6$4* ( ) ;UU A − >$J0."HK'%0LM'"6H#'%0"I'% d 6$bN& A Dc0 6H#'%0"I'% ∆ 0Q$B9&8D"82"8?'%D5D"0aB6J'*[0."I'% ( ) P +_'%> Câu 8 (1,0 điểm). L8'%*[0."I'%@P$"V0G&6] Oxy 1D"8"M'"@N3'% ABCD DX0W*I.LN'%6$4* DQ'"AB() <U;=M 10LN'%6$4*68Q'CI() <U=J >M*0G&6]D5D6d'"DE&"M'"@N3'%1+$J06d'"D 0"N]D6H#'%0"I'% , x y∆ − + = > Câu 9 (0,5 điểm). ]0"].D"S& bN?DeN*)N6f1 ! bN?DeN*)Ng&'"@) h bN?DeN*)N@)'%>iO '%jN'"$\'Dk'%(/DL& bN?DeN0a"].6X>T'"g5D9Ni09&8D"8 bN?DeN6HlD(iOL&DX6/'%*]0 bN?DeN*)N6f@)2"3'%bN5"&$bN?DeN*)N@)'%> Câu 10 (1,0 điểm). "8+&9:0"mDnHK'% 1 1a b c 0"f&*F' Ra b ab c+ + + + = >"S'%*$'", a b c a b c + + ≤ + + + Hết Thí sinh không được sử dụng tài liệu. Cán bộ coi thi không giải thích gì thêm. G@)0\'0"T9$'",oooooooooooooooo:+58n&'",ooooooooooo TRƯỜNG THPT NGÔ GIA TỰ ĐÁP ÁN I>LƯU Ý CHUNG, HP'%nj'D"i*D"d0LM'"+)O*]0D5D"%$?$@P$'"Y'%pDK+?'."?$DX>"$D"i*+)$"GD9$'"()* 0"`8D5D"2"5D'JN6/'%@)6Ep0"M@j'D"86$4*0:$6&> $4*08)'+)$0T'"6J'1!@)2"3'%()*0Lq'> P$+)$"M'""GD2"3'%%$&''JN0"T9$'"2"3'%@A"M'""8[D@A"M'"9&$0"M2"3'%D"86$4*0HK'% S'%@P$."e'6X> II. ĐÁP ÁN, Câu Ý Nội dung trình bày Điểm 1 a "8")*9: ; ; y x x= − + < =C > "?8950@)@A6B0"C < =C DE&")*9:6FD"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> ∀ ∈ −∞ ∪ +∞ < ∀ ∈ 9NOL&")*9:6B'%+$J'0L\' D5D2"8?'% < U= <U =−∞ +∞ 1'%"CD"+$J'0L\'2"8?'% <U= > )*9:6Q0DmD6Q$0Q$ 1 <= x f= = U6Q0DmD0$4N0Q$ 1 <= x f= = − 0,25 ^?'%+$J'0"$\' 0,25 r=B0"C 4 2 -2 5 y x f x ( ) = x 3 -3 ⋅ x 2 ( ) +2 O 1 -1 2 0,25 b G$%$&86$4*DE&6B0"C < =C @)6H#'%0"I'% ;y x= − − () M 1@$J0."HK'%0LM'" 0$J.0NOJ'@P$6B0"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:."SD0"8?*F' z i = + @) z i = − 0,25 3 T'"%$50LC ( ) ( ) ; (8% (8% (8% a b a a P a b b b − = + + ÷ <@P$ 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 $7N2$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 ≤ + + ⇒ + ≤ ∀ ∈ + + − + ≤ − + [02"5D [ ] ; 1 g Ux + ≥ ∀ ∈ 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 DX65O ABCD ()"M'"D"Y'"Z01*[0+\' SAD ()0&*%$5D @N3'%0Q$ S 1"M'"D"$JN@N3'%%XDDE& S (\'*[0."I'%<ABCD=()6$4*H0"N]D DQ'"AD9&8D"8 ;HA HD = >G$M()0LN'%6$4*DE&AB>^$J0L_'% AD a = @) 6H#'%0"I'%SC0Q8@P$65O*]0%XD ; >T'"0"`8a0"40TD"2":$D"X.S.ABCD@) 2"8?'%D5D"0a6$4*M6J'*[0."I'%<SBC=> 1,0 M K D A B C H S H' 8HAx3HD@) 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⇒ = − = NOL& > - > ABCD S AD CD a= = 86X ; > - R > > ; ; S ABCD ABCD a V SH S= = 0,25 MM()0LN'%6$4*DE&AB@)AHyy<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&*%$5D@N3'%SHK0&DX, RR t t a HH HH HK HS a = + = ⇒ = <;= a<=1<=1<;=0&6HlD ( ) ( ) RR 1 > d M SBC a= 0,25 7 L8'%2"3'%%$&'@P$"V0G&6]Oxyz1D"86H#'%0"I'% , x y z− − ∆ = = − 1*[0 ."I'% < = , P x y z+ + − = @)6$4* ( ) ;UU A − >$J0."HK'%0LM'"6H#'%0"I'%d 6$bN&ADc06H#'%0"I'% ∆ 0Q$B9&8D"82"8?'%D5D"0aB6J'*[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$ ( ) <UU= U U;t B AB= ⇒ ⇒ = − − uuur 10&DXn6$bN&<;UU =@)DX@0D.() ; , ; x y z AB pt d − − + ⇒ = = − − uuur 0,25 P$ ( ) ; < U!U ;= !U;U t B AB= − ⇒ − − ⇒ = − − uuur 10&DXn6$bN&<;UU =@)DX@0D.() ; ! , ; x t AB pt d y t z t = − ⇒ = + = − − uuur 0,25 8 L8'%*[0."I'%@P$"V0G&6] Oxy 1D"8"M'"@N3'% ABCD DX0W*I.LN'%6$4* DQ'"AB() <U;=M 10LN'%6$4*68Q'CI() <U=J >M*0G&6]D5D6d'"DE&"M'" @N3'%1+$J06d'"D0"N]D6H#'%0"I'% , x y∆ − + = > 1,0 H N M I D A B C J G$N()0LN'%6$4*CD@)H()0W*"M'"D"Y'"Z0AMND.G$<C=()6H#'%0Lq' '%8Q$0$J."M'"D"Y'"Z0AMND.a%$?0"$J019NOL&NJ//DI1n86XNJ@N3'%%XD@P$ AC1"&OJ 0"N]D<C=<@MAN()6H#'%2T'"DE&<C==>)MDD{'%()6H#'%2T'"DE& <C='\'JM@N3'%%XD@P$JD.<= 0,25 D0"N]D ∆ '\' < U = < U =1 < U;=>D t t JD t t JM+ ⇒ − + − uuur uuur "`8<= > ; ; < U =JD JM t t t D= ⇔ − + + + = ⇒ = − ⇒ − − uuur uuur > 0,25 G$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$=> ZO0G&6]D5D6d'""M'"@N3'%() < U;=1 <U;=1 <U =1 < U =>A B C D− − − − 0,25 9 ]0"].D"S& bN?DeN*)N6f1 ! bN?DeN*)Ng&'"@) h bN?DeN*)N@)'%>iO '%jN'"$\'Dk'%(/DL& bN?DeN0a"].6X>T'"g5D9Ni09&8D"8 bN?DeN6HlD (iOL&DX6/'%*]0bN?DeN*)N6f@)2"3'%bN5"&$bN?DeN*)N@)'%> 0,5 }=:."e'0~DE&2"3'%%$&'*jN() R -CΩ = = }=G$ B ()+$J'D:•bN?(iO6HlDDX6/'%*]0bN?DeN*)N6f@)2"3'%bN5"&$ bN?*)N@)'%€>&gv0+&2"?'•'%9&N, :D5D"(iObN?6f1;bN?g&'"(), ; ! C C :D5D"(iObN?6f1bN?g&'"1bN?@)'%(), ! h C C C :D5D"(iObN?6f1bN?g&'"1bN?@)'%(), ! h C C C 0,25 }="$6X ; ! h ! h ! h B C C C C C C C CΩ = + + = }=s5D9Ni0DE&+$J'D: B () ( ) h ;h - u B P B Ω = = = Ω 0,25 10 "8+&9:0"mDnHK'% 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"$6X R -a b ab c xy z+ + + + = ⇔ + = 0,25 ^DXnQ'% x y z x y z x y z − − − + + ≤ ⇔ + + ≥ 0,25 "Z0@ZO0"`8^ 0&DX x y x y z z xy xy + ≥ ⇒ + + ≥ + "`8^&ND"O D"‚&Lƒ0&DX z xy xy z + ≥ + 0,25 ZO x y z xy z + + ≥ = + iN•x€g?OL&2"$ ( ) ( ) U U ;U;Ua b c = 0,25 - Hết . TRƯỜNG THPT NGÔ GIA TỰ ! MÔN THI: TOÁN "#$%$&'()*+)$,-."/012"3'%240"#$%$&'."5067 Câu. = >"S'%*$'", 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"T9$'",oooooooooooooooo:+58n&'",ooooooooooo TRƯỜNG