TRNG TRUNG HC PH THễNG THANH BèNH 1 ON TAP HOẽC KYỉ 2 KHOI 10. !"#$%& !"# $% &%&% '( ) * +,%-( +./(01 234./(0 '( '( ) )'( 5(67 '( '( 8.9((:;% '( '( ) )'( ++<$!'<(+ '( '( ) )'( Tổng phần chung 2 2,0 3 3,0 2 2,0 7 7,0 +,:7( +=23+ '( '( ) )'( 8<(>(:;% ++<$!'<(+ '( '( Tổng phần riêng 2 2,0 1 1,0 3 3,0 ?(<@A@: = B B= ) )= = C:D(:E:F *+ ,-./ 0'(!" ,12/ 3'(!" )*45678#/ ,9:;/ 3'(!" <hoặc 8,0 điểm* ,=;/ 0'(!" <hoặc 2,0 điểm* GE%::HF I+,%-(F =9/>7?#@AB#$-C9D76%/E#F'5%:G"H9'5%:#$E?9 <gồm 2 câu nhỏ* =9)/-";12I#$A+%7>12J9K =90/5"J#5AL;M#F;#$N7!9#5AL;<gồm 2 câu nhỏ* =9O/P8#@AB#$-AQ#R'AQ#$S<gồm 2 câu nhỏ* I+,:7(F Theo chương trình chuẩn =9T%/,>@AB#$-5%U#5 ,-"9 J+%#%"12!@AB#$-76%VJ"<VJ"MDW J"MV)J"E?9'#$;E?9* =9X%/>#%";MAQ#$SMY@K Theo chương trình nâng cao =9T7/,>'Z5%U#5K ,-"9 J+%#%"12!@AB#$-E76%VJ"<VJ"' DWJ"'V)J"E?9'#$;E?9* =9X7/AQ#$SMY@M[@\7M%$%7K J8KLM ) 8N+OP# Q:(:FR4S F I+TU2V!:W> 2@:F>@AB#$-'7?#@AB#$-/ %K ))OT ) =+ xxx 7K T O ) 0 x x x x + + + 2@:F>J7?#@AB#$-/ 2 3 4 0 2 1 0 x x x + > 2@:)F! >1;# 8#C9>#"W;#$ ]##9[!1.U"D^%C9%+% #$AQ_'AQ9#$%.((.1#%"% ]#VK!""W;+%;. 1`[G7>@=72#a121%9/ !" ( ) 0 O T X 3 b c ( a12 0 T b 0 c )O O ( ) d(( %K -""2#'12#$9DNK 7K -"@AB1%D`eJ9:<Ff;8`@a-*K 2@:*F5"$g;@AB#$-1%99WVJ"Dh".;#$N+%#%" 12 m / ( ) ( 0 ) =+++ mxmx I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF 12 3 sin 2 13 2 a a = < < ữ F1%'#%%'#%M cos 3 a ữ K A ( ) 1, 2A D`AQ#R ( ) :2 3 18 0d x y + = 7K*-"#.%e-89+%_f92AQ#R<E*K 7K)*-"!"2f5+%_C9%<E*K 2@:YF5"R#51%9/ 1 #% 1 1 x x x x + = + A Trong mặt phẳng với hệ tọa độ Oxy. Cho 3 điểm A, B, C không thẳng hàng có tọa độ là A(2; 7) B (1; 2) và C(6;-1) 1) Lập phơng trình đờng cao AH kẻ từ đỉnh A của tam giác ABC. 2) Lập phơng trình đờng thẳng đi qua điểm A và cách điểm B một khoảng bằng 1./// ijjj F I+TU2V!:W> 2@:F>@AB#$-'7?#@AB#$-/ ) ) 0x x x + = OA O ) ( x x + < 2@:F/k8#C9>+%"e# ]#"W8_+%0).1h@(AL#$"H912J9 1%9<#%!"((*/ 0 Xc T) T( TX Xc 3O O Tc b( X0 O) TT X( bb bc O3 XT TT Xb XT T( b( X c( c( XT XT 3) X0 cT 3) 3O &6@7>@=72#a12#a19?#l@h@m"Xh@K&h@a9#n`o% > [ ) O(MT( ' h@#5%`o% > [ ) T(MX( 'p'h@92`o% > [ ) c(M(( K AF12#$97-K 2@:)Fq12;V1%91%e'@r#'=[+%;;#$N 18 π M 2 5 π AF;;#$NAL;S+%9 α 78#/1αd 3 5 D` 2 π <α<π 2@:*F$"I#@Rf[AQ#$S<*/ 2 2 2 4 4 0x y x y+ − − + = N#="D`#F7; F+%AQ#$S<*K As9%_<M(*t[D8#@AB#$-#8@#9[8DhAQ#$St I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF>@AB#$-/f O3) =+x M A-""!@AB#$-f ) )<"*fu" ) u0d(V%J"@=7J#K %\@<Y*/Of ) uc[ ) d0XK-"#.%e;v';#n9!"'#n9w+%<Y*K 2@:YF>;7?#@AB#$-/ 2 12 1x x x − − ≤ − K A@AB#$-/"f ) ,)<")*fu",0d(K-""!@AB#$-V)J"f 'f ) / #x%9 J ) ) K )x x x x + + ≥ K %-"eE`;#$y'#n9!"D`#="1%+%[@\7<* ) ) X c x y − = Kjjjijjj F) I+TU2V!:W> 2@:F>@AB#$-'7?#@AB#$-/ %*zf,)zd)f,7* ) T ) x x > + − 2@:F!"#$97- !"#$%+%()V".1h@( V"/c.1 ')'0'T'X'X'3'b'c V")/.1 '0'0'O'O'X'3'3'3'b'( x/ t[6@;7>@=72#a12D`#9a19?#l@h@Dh;h@{'T*M{T'X|M{3'b|M{c' (|+%)V"K AF12#$97-e'@AB1%'eJ9:G()7>@=72K %n96fl#D 8#C9>`"7`+%%V"K ZP}7!9m#a19?#-e#+%)V"K 2@:)F α α α 2 tan2 +cot2 Rót gän biÓu thøc : A = 1+cot 2 π α sau ®ã tÝnh gi¸ trÞ cña biÓu thøc khi = . 8 A5"7!9#51%9=[ W@y#9eD` α / O 2 2 2 cot 2 cos 2 sin2 .cos2 cot2 cot 2 A α α α α α α − = + 2@:*FP8#@AB#$-AQ#$S<*V#="<OM0*D`C9%_<)M* AP8#@AB#$-#8@#9[8+%AQ#$S<*#!"_<)M* I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF>@AB#$- ) ) 0 x x x− + = + AChøng minh r»ng víi mäi m ph¬ng tr×nh lu«n cã hai nghiÖm ph©n biÖt ) ) < * T X (x m x m m − + − + − + = c)#%";_Z78#%d0'7dT'dO<DE*K5"$g ABC∆ D9W'#^V 19[$%EJ#F ABC ∆ 2@:YF@AB#$-f ) −)<"−*fu" ) −0"d( %K*N"!@AB#$-VJ"fd(KFJ"S %K)*N"!@AB#$-V%J"f'f)#> ) ) ) f f b + = A[@\7<*/cf ) X[ ) dOOK~;NeE`;#$y'#="1%+%<*D`D8#@AB #$-;AQ#J"6Kjjji#jjj F* I+TU2V!:W> 2@:F>7?#@AB#$-/ 2 2 1 0 3 10 x x x + < + − A>J7?#@AB#$-1%9/ +<− +>− )OT TO)T xx xx 2@:F 8`"e#9e#U"ESD12Q#w.G`+%"e#.1h@(#$"e##9a' AQ9#$%.H9nT(.1h@('"H912J9AL#$-7`[EAhE7>@= 72#a12l@h@1%9<BDN`Q*K &h@ a12 [ ] (Mc 0 [ ] (Mc ( [ ] )(M)c X [ ] 0(M0c ( [ ] O(MOc c [ ] T(MTc ) qe dT( %K ?9J9`-•BDN9#$%`-•=[`9#$%"H9%[9#$%#`7eK 7K &6@7>@=72#a12'#a19?#l@h@K K F12#$97-K 2@:)FF;#$N7!9#5 sin cos vôùi tan = -2 vaø cos 2sin 2 P α α π α α π α α + = < < − A€r#.7!9#5 2 2 (tan cot ) (tan cot )P α α α α = + − − T 2@:*F#%";_ZV 1 3 ( 4;4), (1; ), ( ; 1) 4 2 A B C − − − K P8#@AB#$-#qC9;#AQ#R_ZD`#F >;#^8AQ#R_Z AP8#@AB#$-<*VAQ F`_ZK I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF>@AB#$- O) ) −+ xx d +x A~;N"!@AB#$-/"f ) )<")*fu"0d(V%J"EABK %AQ#$S<*/f ) u[ ) ubfO[u)d(K-"#="D`7; FAQ#$S<*K 2@:YF>7?#@AB#$-/ ) ) 0x x x − + < − A@AB#$-1%9'#$V"#%"12#w<)"u0*f ) u)<0"u)*fu",d(K ~;N>!@AB#$-V"e#J"7gD`#-"J"SK %~;N#%"12#n9'#.%ev'#n9!"'@AB#$-AQ9:D`D}@%$%71%9/ [ ) dOfKjjjijjj FB I+TU2V!:W> 2@:F>7?#@AB#$-/ ( ) ( ) ) O ) 3 ) (x x x − + + < MA 0 )x − ≤ f 2@:F 7>@=@2#wJ"#a12l@h@ ;h@;#$N ~ {T(MX(* {X(M3(* {3(Mb(* {b(Mc(* {c(M((| e a12 ) X ( b O 0( &6@7>@=72#a12'#a19?#l@h@K A" F#Ah"H9D`#$97-e+%"H912J9#$n`/ 2@:)F-";#$N7!9#5+d1)( 1O( 1b( AB>7!9#5[d *1<*1< *1<*1< β−α−β+α β−α+β+α 2@:*F$"I#@R#.%ef[∆_ZV_<M)*Z<0M*<(M0* &6@@AB#$-#qC9;#AQ%Z AP8#@AB#$-AQ#$S#8@∆_ZK I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF>@AB#$- ) 0 0 )x x + = − A@AB#$-f ) −)<"−*fu" ) −0"d( AIN"!@AB#$-VJ"fd(KFJ"S AIN"!@AB#$-V%J"f'f)#> ) ) ) f f b + = %_ZV/Zd)'_d)'#$9#9[8_4d 3 KFeE`_ZD`12V_K 2@:YF>7?#@AB#$- ) X b ) 0x x x+ + ≤ + A @AB#$-/ ( ) 2 2 4 0 x m x − + + − = K -";;#$N+%#%"12"!@AB#$-V/ AI%J"@=7J#KAI%J"EAB@=7J#Kjjj8#jjj X FY I+TU2V!:W> 2@:F>@AB#$-7?#@AB#$-/ ) ) c O ( T O x x x x − + ≤ − + MA ) ) 0 0 Ox x− ≤ − 2@:F !"##;+%"e#h@m"OT.1'#2 n!"A1%9/ !" ( ) 0 O T X 3 b c ( 2. ( 0 0 T O ) T 3 0 ) F12#$97-'12#$9DN'"2#+%7>12J9 A&6@7>@=72#a19?#l@h@/{(M)*'{)MT*'{TMb*'{bM(* V7%n9@a#$U".1#$n#$97-K 2@:)F1fd 0 T − D` ) 0 f π <<π KF1)f A5"$g 4 4 2 si sin 2sin 1 2 n x x x π − − = − ÷ 2@:*F$"I#@R#.%ef[∆_ZV_<M)*Z<0M*<(M0* &6@@AB#$-#qC9;#AQ#$9#9[8_4 AP8#@AB#$-AQ#$S#8@∆4_ZK I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF>@AB#$- ) ) ) )x x− + = A@AB#$- ( ) ) ) ) (m x mx m− + + = #-"m!<*V)J"@=7J#=" %/\@<Y*/cf ) uX[ ) dOOK-"#.%e;v';#n9!"'#n9w+%<Y*K 2@:YF>7?#@AB#$- • b ) Ox x x− − − > + A@AB#$->#\ #>\]>]^KPh;#$N`+%"#-@AB#$-#$n V%J"f 'f ) #x%"tJ#5B\ ] \ 1*\ \ #V^ %&6@@AB#$-F#‚+%@%$%7<*KZ8##%"#n9`@dTKjjj8#jjj FV I+TU2V!:W> 2@:F>7?#@AB#$-/ ( ) 2 2 2 7 3 3 5 2 0x x x x − + − − ≥ KA ) O c ) 3x x x − − = + 2@:7>@=@2#wJ"#a12l@h@ ;h@;#$N ~ {T(MX(* {X(M3(* {3(Mb(* {b(Mc(* {c(M((| e a12 ) X ( b O 0( &6@7>@=@2#wJ"#a12'#a19?#l@h@ A&6@7!9m-e##a12l@h@+%7>#$nK 2@:)F€r#.7!9#5/ + = + + 3 3 sin cos sin cos sin cos x x T x x x x AF 3 7 2sin 6cos tan 6 2 6 P π π π = + − 2@:*F: / ) ) (ƒ <MO*d x y M− + = 3 -"#.%e-89+%4nEK A-"#.%e!"2f5+%4C9%E %P8#@AB#$-AQ#R d ′ 2f5+% d C9% M K I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF>@AB#$- T ( bx x + = − A-""!@AB#$-f ) )<"*fu" ) u0d(V%J"@=7J# %<*/f•u[•,Xfu)[uXd(K-"#="D`7; F+%AQ#$S<* 2@:YF>7?#@AB#$- ) ) O 0 ( x x x − > − − A@AB#$- ( ) () ) =++−+ mxmmx K-" m !@AB#$-V)J" #x%/ O ) =+ xx %\@<Y*/Of ) uc[ ) d0XK-"#.%e;v'#$yh'#$yx'#n9!"'#n9w'#="1% +%<Y*Kjjj8#jjj F_ I+TU2V!:W> 2@:F>7?#@AB#$-/ 2 2 2 7 15 0 3 7 2 x x x x + − ≥ − + KA |2x + 3 | = x – 1 . 2@:9%+%T(.1h@T<#F7g"*ALA1%9/ () () 0 0b (c cb O ( (0 )3 b 0( )O T )) )X (3 0O (b b )) cc (c (X (c (O )) 00 )O (b () 0( (3 O O3 (O O (0 (b b 0 0b ) %*&6@7>@=@2l@h@<cb()*M<(0(3*M<(b)*M<03*M<b ))*M<)0)3*M<)b0)*M<0003*M<0bO)*M<O0O3*K 7*F12#$97-e *F@AB1%D`eJ9:K 2@:)F5"$g/ ( ) ( ) ) ) 1 # 1 #% 1 11c c α α α α α + + + = + AF 3 7 2sin 6cos tan 6 2 6 P π π π = + − 2@:*F:$"@(f[_<M*MZ<3M*M<OMO* -"eE`;D`;V+%#%";_ZK AF9DD`EJ#F#%";_ZK %P8#@AB#$-AQ#$S<*#8@#%";_ZK I+TX)!:W> (hc sinh chn bai 5 ho"c bai 6) 2@:BF>@AB#$- Tx + = A@AB#$-/<",*f ) u)<"u*fu)",d(KN"!@AB#$-V% J"#$;E?9K c) AQ#$S ) ) < */ ) b b (C x y x y+ − − − = D`AQ#RE/0fuO[u",d(K N"!AQ#RE#8@frDh<*K 2@:YF>7?#@AB#$- 2 3 4 2x x x− + ≥ + b A@AB#$-/<",*f ) u)<"u*fu)",d(KN"!@AB#$-V) J"f 'f ) 1%/ =+ ) xx 0 %[@\7<*/ ) ) ) ) x y a b − = K5"$g#F >;#^"e#!"7?# ] #$n<*8%#J"6 WqK ```H``` !"# $% &%&% '( ) * +,%-( +./(01 234./(0 ) )'( '( 0 0'( 5(67 '( '( 23!a(&% '( '( ++<$!'<(+ '( '( ) )'( Tổng phần chung 2 2,0 3 3,0 2 2,0 7 7,0 +,:7( 8.9((:;% '( '( ) )'( 8<(>(:;% ++<$!'<(+ '( '( Tổng phần riêng 2 2,0 1 1,0 3 3,0 ?(<@A@: = B B= ) )= = C:D(:E:F *+ ,-./ 0'(!" ,12/ 3'(!" )*45678#/ ,9:;/ 3'(!" <hoặc 8,0 điểm* ,=;/ 0'(!" <hoặc 2,0 điểm* GE%::HF I+,%-(F =9/>7?#@AB#$-C9D76%/E#F'5%:G"H9'5%:#$E?9 '5%:#$E?9U<gồm 2 câu nhỏ* =9)/-"9 J+%#%"12!@AB#$-76%VJ"<VJ"MDW J"MV)J"E?9'#$;E?9* =90/-";12I#$A+%7>12J9K ?9O/5"7?#R#5K =9T/AB#$-AQ#R'AQ#$S<gồm 2 câu nhỏ* I+,:7(F Theo chương trình chuẩn =9X%/5"J#5AL;M#F;#$N7!9#5AL;<gồm 2 câu nhỏ* =93%/>#%";MAQ#$SMY@K Theo chương trình nâng cao =9X7/5"J#5AL;M#F;#$N7!9#5AL;<gồm 2 câu nhỏ* =937/AQ#$SMY@M[@\7M%$%7K c . + A@AB#$-># #>]>]^KPh;#$N`+%"#-@AB#$-#$n V%J"f 'f ) #x%"tJ#5B ] 1* #V^ %&6@@AB#$-F#‚+%@%$%7<*KZ8##%"#n9`@dTKjjj8#jjj FV I+TU 2 V!:W> 2@ :F>7?#@AB#$-/ ( ) 2 2 2 7 3 3 5 2 0x x x x − + − − ≥ KA ) O c ) 3x x x − − = + 2@ :7>@=@ 2 #wJ"#a 12 l@h@ ;h@;#$N ~ {T(MX(*. mxmmx K-" m !@AB#$-V)J" #x%/ O ) =+ xx %@<Y*/Of ) uc[ ) d0XK-"#.%e;v'#$yh'#$yx'#n9!"'#n9w'#="1% +%<Y*Kjjj8#jjj F_ I+TU 2 V!:W> 2@ :F>7?#@AB#$-/ 2 2 2 7 15 0 3 7 2 x x x x + − ≥ − + KA |2x + 3 | = x – 1 . 2@ :9%+%T(.1h@T<#F7g"*ALA1%9/ (). phần chung 2 2,0 3 3,0 2 2,0 7 7,0 +,:7( += 23 + '( '( ) )'( 8<(>(:;% ++<$!'<(+ '( '( Tổng phần riêng 2 2,0 1 1,0 3 3,0 ?(<@A@: = B B= ) )= = C:D(:E:F *+