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Nguyn Quc Tun(0905671232)-Tng biờn ca Website: Xuctu.com Trang LI NểI U Vi 21 chuyờn thng xuyờn gp nhng k thi tuyn chn hc sinh gii lp trờn ton quc Chỳng tụi ó chc lc li v h thng thnh mt quyn sỏch vi y nhng phng phỏp gii nhng loi toỏn ny Do ú, quyn sỏch m cỏc bn ang cm trờn tay s giỳp cho bn c v c bit l nhng bn hc sinh khỏ gii nõng cao nhng k nng v kin thc toỏn hc chng trỡnh toỏn trung hc c s Mc ớch ca chỳng tụi vit quyn sỏch ny l giỳp cho bn c tinh thn t hc Nờn nú c trỡnh by thnh nhng mc cng nh nhng dng toỏn c trng Khụng nhng vy, nú c trỡnh by khỏ p mt cho cỏc em hc sinh To thnh nhng im nhn t hc c bit nhng hc sinh hc nhng loi toỏn v dng toỏn l so vi chng trỡnh hc trung hc c s Cng quyn sỏch ny, chỳng tụi ó ch ng gii thiu n bn c nhng phng phỏp v nhng cỏch gii mang tớnh tru tng mt s dng toỏn Nhng nú m bo c h thng ni dung v phự hp vi cỏc em hc sinh Cú th nhng bi toỏn v s hc v nhng dng toỏn v phộp ly tha cng mang hỡnh búng ca nhng kin thc m tt c chỳng ta u hc chng trỡnh toỏn tip theo Tuy nhiờn, trờn phng din luyn thi hc sinh gii v thi hc sinh gii Chỳng ta hon ton cú th s dng c Khi chỳng ta thờm mt vi bc bin i n thun Cng ti liu ny, chỳng tụi ó kt xut nhng bi toỏn cỏc k thi tuyn sinh hc sinh gii ca nhng ngun uy tớn trờn ton quc v trờn th gii Tt nhiờn nú cng c chỳng tụi h thụng vo nhng chuyờn v nhng dng toỏn ó phõn loi Thc t ti liu ny c chỳng tụi kt xut chy trc tuyn trờn gian hng trc tuyn Do ú, nú c thit k va phi cho s tin dng c v c sỏch ln giỏ c Nờn cỏc em hc sinh, quý v ph huynh ln cỏc giỏo viờn hon ton cú th s dng v hc mt cỏch d dng nht cú th Do õy l mt nhng ti liu phỏt trin u tay Nờn tỏc gi rt mong nhn c s phn hi tớch cc t phớa c gi Mi s úng gúp xin quý v gi v a ch email: quoctuansp@gmail.com Hoc cỏc bn cú th mua bn trc tuyn ny theo s in thoi: 090.567.1232 Nguyn Quc Tun(0905671232)-Tng biờn ca Website: Xuctu.com Trang MC LC CHUYấN - PHN TCH A THC THNH NHN T CHUYấN 2: HON V, T HP 22 CHUYấN - LU THA BC N CA MT NH THC 43 CHUYấN - CC BI TON V S CHIA HT CA S NGUYấN 47 CHUYấN - S CHNH PHNG 61 CHUYấN - CC BI TON V NH L TA-LẫT 91 CHUYấN CC BI TON S DNG NH L TALẫT V TNH CHT 101 NG PHN GIC CHUYấN CH S TN CNG 108 CHUYấN NG D 115 CHUYấN 10 TNH CHIA HT I VI A THC 119 CHUYấN 11 CC BI TON V BIU THC HU T 128 CHUYấN 12 CC BI TON V BIU THC 140 CHUYấN 13 CC BI TON V TAM GIC NG DNG 158 CHUYấN 14 PHNG TRèNH BC CAO 178 CHUYấN S DNG CễNG THC DIN TCH THIT LP QUAN H DI CA CC ON THNG CHUYấN 16 BT NG THC 196 CHUYấN 17 V NG THNG SONG SONG TO THNH CC CP 257 ON THNG T L CHUYấN 18 B HèNH THANG V CHM NG THNG NG QUY 271 CHUYấN 19 TèM GI TR LN NHT, NH NHT CA MT BIU THC 280 CHUYấN 20 PHNG TRèNH NGHIM NGUYấN 302 CHUYấN 21- GII TON BNG CCH LP PHNG TRèNH 320 Nguyn Quc Tun(0905671232)-Tng biờn ca Website: Xuctu.com Trang 123456789 37983
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37 CDEGH IJKJMNOPQRSTOPQRUQQRVOMWXYSZ[J\]^_OP`OaZbORJcOORSdX [J\]^_aRSeOPfgJfYahRJaiORfj^SdOPakOP^lmJn opqstuvwxyzn{k|}X~ZRJa`XOPRJ]P]X~ZX~ZaZOP MOR_X~ZhRYOPSeJagXROgX~Z[\^_][hJ\]agfglXRlQRKJ XY[XK^lmJaZOPMOR_hRYnJXYaR\^Q[SdXMglORJcZ[ hJ\]agn 57847833 CDH lmJXROX~ZaWbalOP|}X~ZXYÔÂĂÊ XUXRn lmJ|XROX~ZhRƠOPaRgbcZXVZn Ă Ư{SeOPRdQXROX~ZalOPX~ZXYÔĐ XUXRn Ư{SeOPRdQ|XROX~ZaZOPMORXYXUXRn Ư{SeOPRdQXROX~Z_aZOPMORalOPăX~ZXYÔâĂê XUXRn Ư{SeOPRdQXROX~Z_hRYalOPX~ZXYÔâĂô XUXRn Ư{SeOPRdQơXROX~ZaZOPMOR_hRYalOPX~ZXYÔâĂâ XUXRn ưbXYÔÂĂÊđâÔĂĐÔâĂêÔâĂôÔâĂâ êôĐĐĂ[hJ\]ag gJfYaalOPXUXRaiORfj[^lmJ|nàRảOPRmOhRJaiORfj[alOP aSeOPRdQag[ãaiOR^áQ^mJaSeOPRdQ_aSeOPRdQ|n CDạDH lmJXROX~ZaWbalOP|}X~ZXYÔÂĂÊ XUXRn lmJ|XROX~ZhRƠOPaRgbcZXVZn Ư{SeOPRdQXROX~ZRláXaZOPMORalOPăX~ZXYÔâĂê XUXRn Ư{SeOPRdQ|XROX~ZRláXhRYalOPX~ZXYÔâĂô XUXRn Ư{SeOPRdQXROX~ZaZOPMORRláXhRYalOPX~ZXYÔâĂâ XUXRn Ă Ă Ă Ă ưbXYÔÂÊđÔâêÔâôÔââ êÊô[hJ\]agn gJfYalag[ãaiOR^áQ^mJfjXUXRXRO[XRằXYX~Z_[XRằXY X~ZaZOPMORalOPaSeOPRdQ_aSeOPRdQ|n CDẳEẵH !"#$%&%'()*+,-./0123*4+-356-789 :;@A 123456789 37983
37 CEFGHIJKLMNOKPQRSTURVFNWXYKPQKZ^\[] K_KL` CEFGHXJKLMNOKPQaLbNWRLcdTeQKfQ` ghVijNWLklIJKLMNOKPQmnLFoKRVQNWpqNLRVFNWIrKPQKZ^s[t K_KL` ghVijNWLklXJKLMNOKPQmnuvaLZRVFNWIwKPQKZ^s[xz^y[ K_KL` ghVijNWLklwJKLMNOKPQRVQNWpqNLuvaLZRVFNWIIKPQKZ^s[szs K_KL` [ [ [ [ [ {|TKZ^\]z}^st^sxz^y^sszs~ t][saHRVd` `HNWQNRVKdRKbNWRTWIXNWijHRVFNW ZKZN`hLHNWQNRVZNWijHRdpfQVdIKLRKLLHNW QNRVIlLZKLRKLLHNWQNRVuvXTuHeN`cHKZTK_KL pfQdFKLFRVFNWNWijHikKpfQlLHKZN` 5784Ă783Â3 CEFGHIJpfQNWijHRSTUÊaLbNWlLPNpHÔ\RNdNƠ` gƯiĐKIJpfQKLRKLuvlLZKLRKLKZăs\ K_KL` gƯiĐKXJpfQXTuHeNKZ^s\] K_KL` âQTVdKZăs\\ê^s\] K_KLpfQôFGHI` CEFGHXJpfQNWijHRFvNNd` gƯiĐKIJpfQKLRKLuvlLZKLRKLKZă\[ K_KL` gƯiĐKXJpfQXTuHeNKZ^\ơ K_KL` \^\ K_KLpfQô âQTVdKZăê FGHX` [ \^\ ơơ\]K_KL` {|TKZăs\\ê^s\]zăê [ ưđRNLZKbNWNLPNWINduvN`WijHRd QNKLMNRNLZVdNWijHô|lRLvNLRRKbNWR_KdFKLFlLH KZIRRViNWNdIRlLZNduvKZRNLRIN`cHKZpdFNLHeQ K_KLô|lRKbNWR_K` 5784Ă783Â3 ChVijNWLklIJKLMNINuvNd` gƯiĐKIJKLMNIRVFNWNKZK_KL` !"#$%&%'()*+,-./0123*4+-356-789 :;@A 123456789 37983
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37 LMNOPJQERSJT BCDEFHIEFJKJ \^]U V]VUWWXYUWWU \^]U V]VUWWXYZUWWX_X[ \^]U V]VUWWXUVUWWX \^ Z]U VUWWXU[VZ]_ UWWX[ \^ Z]_ UWWX[Z]VUWWU[ `a78bbcdefgh1idjklmgndeolmdpq rcd9sthuvw78txy9a 78 z{|}~93793~9r3u79 9578q 13 t~TENRMNMEEET ^] _X LMNOPJQERSJT BCDEFHIEFJKJ... !"#$%&%'()*+,-./0123*4+-356-7 89 :;@ 123456 789 37 983
37 NPO QGCO QH NP IO Q EO QHJQGKOD NP IO QHJ QHKOEIOD QHJQKDOD LHKOEIOD QHJQMEOD NP IO QHQCOEJE LHKOEIOD QHLEOEJP IOD QCOE QHJE LHKOEIOE LHJE NP IO QCOE QHJE LIDOM LDOJE NP IO Q DOM QCOE LDOQHJIOD LDOM QCOE Q DOQHJ C C D D D D D D E RST9UVWRXY78VZ[9\ 78 ]^_`ab93c779d7]9a 78 1e3fgVhaijklmnopqlrsoltqusvolwnlnlmnoxy {POz... !"#$%&%'()*+,-./0123*4+-356-7 89 :;@A 123456 789 37 983
37 Q NGRDMOHIENOHIMOHPNGRDKOLN OKL E LM HI Q KKLJOPO PHIMOH F STUVWXWYZ[\ KLPHI]K OL^HI_OH Q KLRHIKRHILOHIIPH Q KL ]RHI_H R ILOHI_PH F F IH P KRHIPRH P i LRHIPRH `ZabccdefghcXWYZ[\ KLRRHHIH jefkWWlHGTZWmYWln opqrstThcXuYTYv|YwWXTxYyWekWXTzWy{\ WJ}PNO| ~JPDNOGEDNOEDNO|EDNOERG| 5 784 783 3 WycdT|cdTvXTa~XTcdX... M G NLHw FD NDw cDLwcwG LC FCH M wGFLw NLC FC NLCH M wLCG FLHFCG FLH M wG FLL HG FL HG NH M wGJNKFLL HG NJFKL HG FJNKH 78 k1k !"#$%&%'()*+,-./0123*4+-356-7 89 :;@A 123456 789 37 983
37 1C3DEFGHIJLMNOPQRMSTPMURVTWPMXOMOMNOPYZ acb[ ^_b\ d`]b] ^`[bd\ efgOhijOhklk mMnOopPZRqRVr s`ts\uMvOhwXOhMkxyRzTSTPMURtSTPMURuMvOh R{OhMkxyOhW|}ORzOhuMvOhR{OhMkxyM~WP... !"#$%&%'()*+,-./0123*4+-356-7 89 :;@A 123456 789 37 983
37 MON PN PH MO INB JNKPINC JND KPIND PNPHK MONN IE JHKINE PHKPNDINE JHKPIND PNPHK MO IND PNPHKINJHKINF PNKPND INJHKIND PNPHKPIND PNPHK MO IND PNPHKLINC JNF PND JNKPINE JND KPHQ MO IND PNPHKINC JNF PNE JNPHK B C R9379ST UVWXYZ[\WW]^_`a NEb PH PNEcPD PH`[de NB PND PHg NB PNC PHg Nf PNF PHg NC PNPHg Nf PNPHg h XijW]`[k`ZlW[j`amnoDpopH qr78stuvw1xyz{|} 1~3T... qrsbtuvbtwxw PMIPERpM PH G E QPMHPRHM PPERHM PH QPPEMHPRHMPEMHPRH Q CPMKDCPMEDE C DC D Z[\^_`abcde`eefgc`heigjc`kb`b`abcl~ gPE ME MIPRI {OQEPE MIPMJ 5 784 783 3 gygezb`bmck{w|bf}w~ !"#$%&%'()*+,-./0123*4+-356-7 89 :;@A 123456 789 ... d`a^`a ONN I P FKINPKINPHKPHDf OLI NNPHKQLINP FKINPKQPHDf O IND PHK N PIND PHN P DFKPHDf ZND PHNPHDO [X]XYZ[\WW]^_`a !"#$%&%'()*+,-./0123*4+-356-7 89 :;@@ 123456 789 37 983
37 MPDNFGCHDNQGCHQGCI MPNC FGJJQGCI MPNC FGK MP DNQ JHDNFJH MP DOC QGLOQIHDOC QGLO QGKH M P DOQ CHDOQIHDOCQGLOQIH 1R3STUVWXYZ[\]^_`[ab^[c`dbe^[f][][\]^gh M POJ QKOi QjOC FKOQG sqrdgtuL^bvqw^... d` 1C3DEFGH£JLMNOPQRMSTPMURVTWPMXOMOMNOPY ¥c]b[ ^\b\ ^¤b] d_bd efgOhijOhklk mMnOopPZSTPMURR{`OhMkxywXo]O}OR{PM¦TVrwXo^]iS{PT R{Z !"#$%&%'()*+,-./0123*4+-356-7 89 :;@A 123456 789 37 983
37 MRFN GEN GHN SINSJ MRKNGFLKFNE SONF SPNSQL MR FND SKOGDLNE SKPGFL ONF SKQGFL PNGFQ abO`DR`E aOR^ TUVWXYZ[\]bdbPQ``FFPORR`IHc bdbPR`_ eb`FQRJ eQR`D D E F fgh]MRFND GENE GHNF SINSJRKNGFLF... L SPF SKE GP L SKPQSON LGE abOQR^F abORD S R` P Q O ^ hthqpp\V n]bbdbEQ`OR_ c bdbPQRR`EI ^F beRF bbEP`R` e PR^F !"#$%&%'()*+,-./0123*4+-356-7 89 :;@A CDFGH 123456 789 37 983
37 TWJIUI XKULJIVI XJIVLJMUVLNOPQULRVXNSPNUX IV LJS 1Y3Z[\]^_7Z[ `a]bcdefghijeFkheljmknheogegefghp tWquXJrquXNrquXKrquXsrXJK ~kjG|gF| vwxgyz{gy|}| tWquXJrquXNrquXKrquXsrXJK... Q CQKNQjH MPOCDNQiHC MP DONQiH OC MPD OOF GOHC Qi OC MP DOC QiOFGHC 9Yfq^pe^]`^[nqrq]n``[o]n[]na]n^[c` ][ldbeh !"#$%&%'()*+,-./0123*4+-356-7 89 :;@A 123E456 789 37 983
37 N PO QGO QHO IGOQJ NPO QKGO IEOE LQKMOE IGOQJL NP O Q EOKDOIJLQKDOIJLE NP KO QDOIJLE C C C E D D E 1R3STUVWXY Z[\]^_`[ab^[c`dbe^[f][][\]^gh NPKOEQlEQmELKOQlQmLEQKOlQlmijkLE nop]qrs]qtut