hệ thống bài tập toán lớp 10 nâng cao

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B A x C (x A vaø x B) ∈ ⇔ ∈ ∉ b - ( 9 9∪? 9 ?  ? 9 ? 9 B A B A A \ B C = K7"Z( B A x x C C A B. = = A B x x B A C C . ]8" ##(QJRJ KKLBM*. 4#$C9t? x A \ B (x A vaứ x B) K7"Z( A \ A = A\ A = A B = = M> M+^]4='([('U; 5;3-ZD4Z8#4'*a; P'RC - 2 A {x N |x 7 vaứ x 10}. = < ` B {x N |x 15 vaứ x laứ boọi cuỷa 2} = ( C {x N | x 4 vaứ x laứ boọi cuỷa 3} = M+_]4='([('U; 5;3-ZD4Z8!2('C - A {0, 1, 4, 9,16, 25, 36}. = ` B {3, 5} = ( 1 1 1 1 1 C 1, , , , , 4 9 16 25 36 = Z 1 1 1 1 1 D , , , , 2 4 6 8 10 = f { } E (0, 2); (1, 3) = u v@ { } 9, 36, 81,144 { } G 3, 9, 27, 81 = M+`wS'x- `-1 $%4Wy([('U; 5;3-C - 2 A {x | x 3x 2 0} = + = 7$ B {x | x 2 0}. = = ` 2 B {x | x 1 0} = + = 7$ 2 F {x | x 4 0}. = = ( G {2, 3} = 7$@zT:b{ DM+a 1'U; 5;9@n-:`:(:Z:fq -I9(G`-1 4a'U;(1| `IG`-1 4a'U;(1(<-9( 0yb; P'R| (IG`-1 4a'U;(1(<-9( - 4" /'d; P'R| M+b>%9?}9?}9t?}?t9:`4='j -I9@KT:lM}?@z:b{ `I9@K:d{}?@K:lM (I9@nF~IFoq?@nF~ITFq d 9 ? 9t?   @>0cMd=>MeD QJT"!" #+fgV$'>%'/'(Q([(4[',(<-F!N $%3i(G •- ‚LFC -I MK MK xf xg y = F[(!, * 47$( r* 4CuKFM7$KFM(YF[(!, 7$ MK ≠ xf  `I MK T xfy n =  l]D4#ƒ' >w@'U;F[(!, (<-uKFM l]D4( „' >w#$C MK ≥ xf  (I MK MK xf xg y = F[(!, * 47$( r* 4CKFMF[(!, 7$uKFMA ZI MKMK xgxfy ±= F[(!, * 47$( r* 4C MK ≥ xf 7$ MK ≥ xg  0h25(Y" #+fg 1 $%3iuF[(!, 'aB $%3i!E`4='aB= MKMK:} TTT xfxfxxKxx <⇒<∈∀  $%3i ,( `4='aB= MKMK:} TTT xfxfxxKxx <⇒<∈∀ ‚CNFS'3…`4=' 4a(<- $%3i:'-(P' …( 4C i&((jfg T T MKMK xx xfxf − −  l=K‚MA@AI3i!E`4= l=K‚M•@AI3i ,( `4= $+fg"kEl 1 $%3iuF[(!, 'aX $%3i( „uKFM@uKFM  $%3i#ƒuKFM@uKFM ‚"L l$%3i( „ U'†('#$%'†(!i4F l$%3i#ƒ Ui('18!&#$%')%!i4F 3+fg2Q"Z( #+fg[m#Tn2 l=-A' > I3i!E`4=CKLBM l=-•' > I3i ,( `4=CKLBM 2W(!+fg baxy +=  "*oG' N7‡!E' ,@-Fl`7$@-Fˆ`E4F1[!4 -4; P!' +j% ; ZD4'†( 1$  P(O#84#$!E' , $%3i!‰( 1 ^+fg2Q"# ‚"2,p"%I'f(*+*o lw[(!, !r (<-KM#$ lw[(!, '†(!i4F7$ D(<-KM lw[(!, '18!&([(4-1!4N%(<-KM7D4'†('7$'†( 1$ K=(GMw[(!,  ' a%%&'3i!4N%(<-KM!N7‡( 1( . F[( lVU;`Q`4=' 4a l]‡!E' ,(<-KM Š"LC l=-A' >KM(G`"#‹%x-#a l=-•' >KM(G`"#‹%x-Fi o   M> M+>%'U;F[(!, (<-([( $%3i3-C -I p b T − + = x x y `I MTMKbK TMbK −− −− = xx xx y (I MMKbTK bd xx xx y −− −+− = ZI boT  T ++ + = xx x y fI T −−−= xxy M+B Q13['3…`4=' 4a7$7‡!E' , $%3iC -I b +−= xy `I T −= xy (I xzy T −+= ZI b T += xy fI obT T −+−= xxy M+$wS''. ( „#ƒ(<-([( $%3i3-C -I bT T −+= xxy `I x y  = (I TT ++−= xxy M+3w[(!, -:`(<-!E' , I3i@-Fl`'1([(' 5;3-C -I4x-9K}TM7$!4N%?KT}M `I4x-9K}M7$3131'†(F (I4x-KT}oM7$(G 3iG(`j:o ZI4x-ŒKd}TM7$7G(7D4!' + o T  + − = xy M+^ >%`i $%3i`U( /'(G!E' ,#$`i!' +(•' -'84`i!r (<- > 7  Ui(#$%')%!i4F:`4='%&'!r (<- > 7#$9Kb}M M+_w[(!, KM  T ++= bxaxy '1([(' 5;3-C -I4x- -4!4N%9K}TM7$?KT}M `IG!r ŽK}M (I•-K}dM7$(G'!&`j M+`>%KM cxaxy +−= d T  -I4x-9K}TM7$?KT}bM `IG 1$ !&!r #$b7$!4x-KT}M @Oq=>OqD Br@As I*+2YE8QC #,-.(Xt2Q"Z(#Tn2mu l=  ≠ a C; ^'> (G 4%Z /' l=-@}  ≠ b C; ^'> 7 4% l=-@}`@C;'73i 4% 2,-.(Xt2Q"#  T =++ cbxax  ‚=-@C;''•' P ;'`U( /' K4Q4'^'… 'aM ‚=  ≠ a C l  <∆ C; ^'> 7 4% l  =∆ C;'(G 4%*S;  l  >∆ C;'(GT 4%; )`4' a b x T ∆−− = 7$ a b x T ∆+− = m   !EF=&(-43i T } xx #$([( 4%(<-;' T  ax bx c + + = * 47$( r* 4' 1Q%‰ ' (C a b xx − =+ T 7$ a c xx = T   $(v8[*J(2Q"Z(*+2Q"#  #,-.(Xt"4#w(X'.]Z8.(X!(8[(g K;x. MKMK xgxf =  "Cl2'!I*C MK ≥ xf l?> ; ^ -47=:4Q4'>% 4% lB=' 5;!I*7$!--'U; 4a%(<-; ^'>  "Cl    ≥= <−= MKMKMK MKMKMK xfkhixgxf xfkhixgxf  K;x. MKMK xgxf =    ⇔ = −= MKMK MKMK xgxf xgxf 2,-.(Xt]x. MKMK xgxf = •@A   T ( ) ( ) ( ) ( ) g x f x f x g x ≥   ≥   =  ".I%"C  l2'!*(G •- l?> ; ^T7=4Q4'>% 4% ",-.(Xt"4#wyz8   K".I  l2'!I*%‘3i(G •-  l•!E%‘3iE44Q4'>% 4%K( 0J!I*M ],-.(Xt(X\.J,-. MK Td =++ cbxax K".I   l2' I T ≥= tkđxt   l -'7$1;'KM4Q4'>%'@AF KLF=".I2J( MKMK xgxf ≥ { MKMK xgxf ≤ { MKMK xgxf > { MKMK xgxf < *+ MKMK xgxf ≥ { MKMK xgxf ≤ { MKMK xgxf > { MKMK xgxf < "|.(,-.(h.IJ,-. (XtDj(#[}]Z8~m•(+]Z8~€{•{ ≤≥ } • 3J(2Q"##w N4Q4 ;'`U( -4 -4’:'-' ZYC;;' =:;;(&:;;!2'’; †]4(( 6;;$1 (O'“' &(7$1([(; ^'> (†' N M> M+4Q47$`4#U;'C -I mxxm TT T +=+ `I TMK −+=− mxmxm (I TcMK T =−+− xxm ZI MbKT T =+++− mxmmx c   M+>%%!N;'3-(GT 4%'[4Z/ bMTKMK T =−+−++ mxmxm M+$>%%!N`;'3-7 4%C T K TM TK M T m x m x m − + + + > M+3C 1;'%F T ˆTK%lTMFld%l€@, %!N; ^'> C -IGT 4%; )`4'`IGT 4%'[4Z/ (IGT 4%!")%ZIGT 4%; )`4'' 1QC o T T  T −=+ xx  M+^ 1; ^'>  bMKd T =+++− mxmmx -I, %!N; ^'> (GT 4%'[4Z/ `I, %!N; ^'> (G 4%$/;b#P 4%*4- (I, %!N; ^'> (GT 4%3-1( 1C b  T =+ xx M+_ 1; ^'>  TTMbTK TT =++++− mmxmx -I, %!N; ^'> (GT 4% T } xx ' 1Q T Txx =  `I4Q43R; ^'> (G -4 4% T } xx ‰'>% ' (#4a 4s-([( 4%!&( #U;7D4' -%3i% M+`4Q4([(;'7$([(`;'3-C -I dcT =+− xx `I pTc€ T −=+− xxx  (I Tob Td ≤−+ xx  ZI MbTMKcTK T >−−+ xxx  fI oT +≤− xx uI T  T ≤ − + + x x x x I dbbTT ≥−−− xx I xxxx bbMbKT TT +=−+ ; I2'’; † Cb T ≥+= tđkxxt M+a>%([(4[',(<-F' ”-%‰%e4`;'3- I  T < − x x  TI bTT +<− xx bI T T  T d d bx x x < − − + dI x x x > − +   oMT T b b d x x − − − ≥ b T mM T  Tx x ≥ + − M+b4Q4 ;'7$`;'3-C -I    =− =+ T md TT yx yx  `I    =++ =+++ o € TT yxxy yxyx  (I    =+ = T€ pm TT yx yx ZI    =− = oo Td TT yx yx fI    =− =− xyx yxy bT bT T T uI    =+ =+ b dT TT TT yxyx yx I      + < − −<+ o b d bT b € o b xx x x x I      +>+ +< + dpT€odT ToT T b€ xx x x €   @=Md‚ƒ=>MdOqD Br@As MZ(„.(4" #M25}(,-.,-. • ?4=!k4'^!^`!'' ((P(I%-%&'!4" 4N 4a 2M(…fC]D4 -43i-}`* )%' >C ba ba  T ≥ +  X/g@HFQ--@` KyX….]D43i* )%}'-(GC n n n aaa n aaa   T T ≥ +++ X/g@HFQ-* 47$( r* 4C n aaa ===  T ";\.M((tB{" #fg • -43i* )%-7$`(G'k* !k4' >'.( -`!8'* 4-@` • -43i* )%-7$`(G'.( * !k4' >'k-l`!8'V* 4-@` ;Z8" #!(4"2Q"Z( -I, #JCKLBM `I]U!†!, #J4Q4`;'C l?;''.( l?;'( -%‘ l?;'( -’'1Z/4[',''!i4 $;Z8" #(#(4"2Q"# -I, #JCKLBM `I]UZ†C l?;'' ^'.( l`;'`U( -4 ‚ : T >++∈∀ cbxaxRx    ⇔ > <∆   a ‚ : T <++∈∀ cbxaxRx    ⇔ < <∆   a M> M+4. -I bbdd abbaba +≥+ `I cabcabcba ++≥++ TTT (I abcaccbba €MMKMKK ≥+++ 7D4 }} ≥ cba  ZI pM  MKK >++++ cba cba 7D4 }} > cba p fI a a b b a c b b a +++ T T T T 7D4 }} > cba M+C>%V7$(<- I3iK=(GM -IuKFM@FKFM7D4 x `IuKFM@TFKbFTM7D4 b T x (I T MK + ++= x xxf 7D4FAT M+$wS'Z/`4N' (3-C -I ( ) ( ) ( ) 2 5 6 2 1 4 3 x x x g x x + = `IuKFM@bFKTFlcMKpbFM M+34Q4([(`;'3-C -I 9 5 1 x x + > `I 3 47 4 47 3 1 2 1 x x x x > (I T T xxx ZI Tdb T ++ xxx @=cPD Ă ÂĂÊÔ ƠƯĂĐă âÊêôƠƯĂĐă Ă ơÊ-đĂ ơÊ ƠƯĂĐă ĂàêảãđđÊáƠƯĂĐă M> ƠđạằẳẵắạẵắƠẵắặầẩẫạấạƯậèạẫăẵẻẽẽéẹềẫểẻễẵạếắạệàẵìỉ ầƠ b b To To bo do d d bo do bo To do b b b d b To do do bo bo b d d d bo bo bo bo ẫăặạĩệíĩịìẫầắòêỏẵõíĩịìẫ ằăóọầồổƠ 1 ẳẵắổạỗẵằốẵ 1 ẳẵắổạỗẵằốẵặ ẹăộẫờởẳẹềẫẹỗằăỡóọẵạồẵớợịớạùẵắồổìẵắẹềẫẹủẹầĩệạẵắ ƠđạũầĩệẹúằẳẵắổạỗẵằốẵốẵặắạợổầổẵạùẫƠ ạú Đạẳẵắ ốẵƯẵĩă ốẵặƯụĩă zm}{ p Từ T zp}p{ Tdddừ b zpT}pd{ p dTTTừ d zpo}pc{ m bbdừ ửẵắ @do ừ -M ữằĩứíựạòẵạẹỳốẵ ằăữằĩứíựạòẵạẹỳốẵặ (M ữằĩứíựíùỷẵắắặổạẩẹốẵ ỹăữằĩứíựạòẵạởậ ƠêíỳỹĩỳẹạĩĩờủọƯíỏẵõíỳỹĩầẹăẫạíùýẹũầĩệẫƠ dd db dT ddo dp om oT obd ooo om omd ocT ocd o oc o op op opb opd m mb mo mT [...]...Trng THPT Nguyn Cụng Tr CNG ễN TP TON 10- NC a) Tinh sụ trung binh, sụ trung vi va mụt b) Lõp bang tõn sụ ghep lp gụm 6 lp vi ụ dai khoang la 4: nhom õu tiờn la [40;44) nhom th hai la [44;48); Bai 4: Thng kờ im toỏn ca mt lp 10D1 c kt qu sau: im 1 2 3 4 5 6 7 8 9 10 Tn s 1 2 4 3 3 7 13 9 3 2 Tim mụt ?Tinh sụ iờm trung binh, trung vi va ụ lờch chun?... la trung nhau BI TP: 2 3 3 2 3 1 ; ; 1; ; ; ; Bai 1: ụi cac sụ o goc sau ra ụ: 3 5 10 9 16 2 Bai 2: ụi cac sụ o goc sau ra raian: 350; 12030; 100 ; 150; 22030; 2250 Bai 3: Mụt cung tron co ban kinh 15cm Tim ụ dai cac cung trờn ng tron o co sụ o: a) 16 b) 250 c) 400 - 11 - d) 3 Trng THPT Nguyn Cụng Tr CNG ễN TP TON 10- NC Bai 4: Trờn ng tron lng giac, xac inh cac iờm M khac nhau biờt rng cung AM co... sin15 ) a) A = sin Bai 9: Khụng dung bang lng giac, tinh cac gia tri cua cac biờu thc sau: a) P = cos 2 3 cos + cos 7 7 7 b) Q = cos Bai 10: Rut gon biờu thc: - 14 - 2 4 6 + cos + cos 7 7 7 Trng THPT Nguyn Cụng Tr sin 2 + sin a) A = 1 + cos 2 + cos CNG ễN TP TON 10- NC b) B= 4sin 2 1 cos 2 2 c) 1 + cos sin 1 cos sin B/ HèNH HC CHNG I: VECT 1) + Hai vộc t c gi l cựng phng : nu giỏ ca chỳng... p = 1 (a + b + c) 2 BI TP: Bai 1: Cho ABC cú c = 35, b = 20, A = 60 0 Tớnh ha; R; r Bai 2: Cho ABC cú AB =10, AC = 4 v A = 60 0 Tớnh chu vi ca ABC , tớnh tanC Bai 3: Cho ABC cú A = 60 0 , cnh CA = 8cm, cnh AB = 5cm a) Tớnh BC b) Tớnh din tớch ABC c) Xột xem gúc B tự hay nhn? d) Tớnh di ng cao AH e) Tớnh R Bai 4: Trong ABC, bit a b = 1, A = 30 0 , hc = 2 Tớnh Sin B Bai 5: Cho ABC cú a = 13cm,... phng trỡnh ca ng thng (D) trong cỏc trng hp sau: a/ (d) qua M (1; 2) v vuụng gúc vi t : 3x + y = 0 x = 2 5t y = 1+ t b/ (d) qua gc ta v vuụng gúc vi t Bai 10: Cho tam giỏc ABC cú nh A (2; 2) a/ Lp phng trỡnh cỏc cnh ca tam giỏc bit cỏc ng cao k t B v C ln lt cú phng trỡnh: 9x 3y 4 = 0 v x + y 2 = 0 b) Lp phng trỡnh ng thng qua A v vuụng gúc AC Dang 2: Chuyờn ụi cỏc dang phng trinh ng thng x =... = 0 va (d2): 6x 4y 7 = 0 x = 1 5t y = 2 + 4t x = 6 + 5t y = 2 4t x = 6 + 5t d) (d1): 8x + 10y 12 = 0 va (d2): y = 6 4t c) (d1): va (d2): Dang 4: Goc va khoang cỏch Bai 1: Tinh goc gia hai ng thng a/ (d1): 2x 5y +6 = 0 va (d2): x + y 3 = 0 x = 6 + 5t y = 6 4t b) (d1); 8x + 10y 12 = 0 va (d2): c) (d1): x + 2y + 4 = 0 va (d2): 2x y + 6 = 0 Bai 2: Cho iờm M(1; 2) va ng thng... 3 Bai 10: Cho ng thng ( ): 2x y 1 = 0 va iờm M(1; 2) a/ Viờt phng trinh ng thng ( ) i qua M va vuụng goc vi ( ) b/ Tim toa ụ hinh chiờu H cua M trờn ( ) c/ Tim iờm M ụi xng vi M qua ( ) NG TRON 1 Phng trỡnh ng trũn tõm I(a ; b) bỏn kớnh R cú dng : (C ) : ( x a ) 2 + ( y b) 2 R 2 (1) 2 2 x + y 2ax 2by + c = 0 hay (2) 2 2 2 vi c = a + b R - 21 - Trng THPT Nguyn Cụng Tr CNG ễN TP TON 10- NC... thỡ phng trỡnh trờn l phng trỡnh ng trũn Bai 1: Trong cac phng trinh sau, phng trinh nao biờu diờn ng tron? Tim tõm va ban kinh nờu co: a) x2 + 3y2 6x + 8y +100 = 0 b) 2x2 + 2y2 4x + 8y 2 = 0 2 2 c) (x 5) + (y + 7) = 15 d) x2 + y2 + 4x + 10y +15 = 0 Bai 2: Cho phng trinh x2 + y2 2mx 2(m 1)y + 5 = 0 (1), m la tham sụ a/ Vi gia tri nao cua m thi (1) la phng trinh ng tron? b/ Nờu (1) la ng tron... (C ) bit: x = 1 + 2t : y = 2+ t va (C): (x 1)2 + (y 2)2 = 16 Bai 6: Viờt phng trinh ng tron i qua A(2; 1), B(4;1) va co ban kinh R = 10 Bai 7: Cho I(2; 2) Viờt pt ng tron tõm I va tiờp xuc vi ( d ): x + y 4 = 0 - 22 - Trng THPT Nguyn Cụng Tr CNG ễN TP TON 10- NC Dang 3: Lõp phng trinh tiờp tuyờn Bai 1: Lõp phng trinh tiờp tuyờn vi ng tron (C) : ( x 1)2 + ( y + 2) 2 = 36 tai iờm Mo(4; 2) thuục... Hypebol (H) la: Hai tiờu iờm : F ( p ;0) 2 ng chun : x = p 2 BI TP: Bi 1: Lp phng trỡnh chớnh tc ca Hypebol (H) trong cỏc trng hp sau: - 25 - Trng THPT Nguyn Cụng Tr CNG ễN TP TON 10- NC a/ di trc thc l 8 v tiờu c bng 10 b/ Tiờu c bng 20 v mt tim cn cú phng trỡnh 4x 3y = 0 Bi 2: Lp phng trỡnh chớnh tc ca Hypebol (H) trong cỏc trng hp sau: a/ (H) cú mt tiờu im l ( 5; 0 ) v cú trc thc bng 8 b/ (H) . r-'. ( /'!2('(<-'U; 5; ]XC9@nhhhhhhhhq Là tập hợp khôpng có phần tử nào,kí hiệu là ∅ VJC∅@ { } { } . ≠ ∅ QJ"' # A. B = = M> M+^]4='([('U; 5;3-ZD4Z8#4'*a; P'RC - 2 A {x N |x 7 vaứ x 10} . = < ` B {x N |x 15 vaứ x laứ boọi cuỷa 2} = ( C {x N | x 4 vaứ x laứ boọi cuỷa 3} =. 36}. = ` B {3, 5} = ( 1 1 1 1 1 C 1, , , , , 4 9 16 25 36 = Z 1 1 1 1 1 D , , , , 2 4 6 8 10 = f { } E (0, 2); (1, 3) = u v@ { } 9, 36, 81,144 { } G 3, 9, 27, 81 = M+`wS'x-