[Tailieupro.com] - Tổng hợp công thức giải nhanh trắc nghiệm Toán của thầy Đoàn Trí Dũng

1 Truy cập website www.tailieupro.com để nhận thêm nhiều tài liệu TUY N T P C˘NG THÙC GI I NHANH TR C NGHI M TO N https://www facebook com/tailieupro/ VN 1: C C C˘NG THÙC TH T CH TÙ DI N KH´: https://www facebook com/tailieupro/ Bi¶nso⁄n: onTr‰Dơng-i»n tho⁄i: Cỉngthøc1:V= S:ABC https://www.facebook com/tailieupro/ abc p 0902.920.389 1cos2cos2cos2’+ coscoscos’ \ Cæng thøc 2: VABCD = 6AB:CD:d (AB; CD) sin AB; CD 2S1S2 sin (Cæng thøc th” t‰ch gâc nhà di»n) Cæng thøc 3: VSABC = https://www faceb o ok.com/tailieupro/ a p2 Cæng thøc 4: Th” t‰ch tø di»n •u VABCD = 12 p https://wwwCỉngthøc5:Th”t‰chtødi»n.facebookgƒn•u:V ABCD= com/tailieupb 2p (2 + 12 ro/ 22)(b2+22)(2+2b2) https://www facebook com/tailieupro/ https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ VN2:G´C×˝NGTH NGVMTPHNG: https://www\[.facebook.com/tailieupro/ Gâc lo⁄i 1: (SA; (P )) = SAH (Gâc giœa c⁄nh b¶n v m°t phflng ¡y) \ [ Gâc lo⁄i 2: (SB; (SIC)) = BSF (Gâc giœa c⁄nh b¶n v m°t phflng øng chøa ÷íng cao SI) https://www\\.facebook.com/tailieupro Gâc lo⁄i 3: (SK; (SDE)) = KSG (Gâc giœa ÷íng cao SK v m°t b¶n (SDE)) V https://www facebook com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro N3:G´CGIÚAHAIM \ TPHNG: [ https://www\[.facebook.com/tailieupr Gâc lo⁄i 1: ((SAB); (P )) = SCD (Gâc giœa m°t b¶n v m°t phflng ¡y) Gâc lo⁄i 2: ((SAB); (SCD)) = KSJ (Gâc giœa hai m°t b¶n câ hai c⁄nh song song AB v CD) \ \ Gâc lo⁄i 3: ((SM N); (SHN)) = OP M (Gâc giœa m°t b¶n v m°t phflng øng chøa ÷íng cao SH) VN https://www.facebook.com/tailieupr 4:CCVN V MTCU: https://wwwculoi1:CĂcnhA;B;Dcũng.nhfacebooknSCdữợimtgõcvuổng.thcom/tailibĂnknhmtcuR=eSCupr Mt https://www.facebook.com/tailieupr https://www.facebook.com/tailieupr https://www.facebook.com/tailieup https://www.facebook.com/tailieup Truy cp website www.tailieupro.com để nhận thêm nhiều tài liệu SA M°t cƒu lo⁄i 2: N‚u SA vuæng gâc vỵi ¡y th…: R = RD + https://www.fpa2cebook.com/tailie3 + N‚u ¡y l tam gi¡c vuæng th… RD = https://www + Nu CĂc vĐn ã cn ỵ v• RD: p c⁄nh huy•n v n‚u ¡y l tam gi¡c •u th… RD = upro/ f acebook com/tailieupro/ ÷íng ch†o +N‚u¡yl…nhvngth…RD= ¡y l h…nh chœ nh“t th… RD = a 21 https://wwwN‚u¡yltamgi¡cc¥ncâgâc120.facebook cnhbảnbngthcnh.Ăycom/tailibng3cặnR =.eupro/ + + Nu D abc Ăy l tam gi¡c th÷íng th… ¡p dưng cỉng thøc Heron: R D = https://www.facebook com/tailieupro/ ()(b)() M°t cƒu lo⁄i 3: N‚u O:ABC l tam di»n vuæng t⁄i O th… R2 = 14(OA2 + OB2 + OC2) https://wwwMtculoi4:NuchõpcõcĂccnh.facebookbảnbngnhauth:R=.SAc om/tailieupro/TrongõOtƠmcaĂyv: + N‚u ¡y l tam gi¡c 2SO •u th… O l trồng tƠm, trỹc tƠm https://www facebookimcnhhuyãn com/tailieupro/ + + N‚u¡yltamgi¡cvuængth…Ol trung N‚u ¡y l h…nh vuæng, h…nh O l giao i”m hai ÷íng ch†o v l trung i”m mØi ÷íng M°t https://wwwcƒulo⁄i5:N‚uhaim°tvng.gâcfacebookvỵinhauth…R =R +R cABo m/tailieupro/trongâABgiaotuy‚n 2 2 M°t cƒu lo⁄i 6: Châp S:ABC tng quĂt cõ chiãu cao SH v tƠm Ăy l O th ta giÊi phữỡng trnh: (SHhttps://wwwx)2+OH2=x2+R2mx.VợifacebookxtmữổctacõR2=x2.+com/tailieupro/R2 D 3V Mt cƒu lo⁄i 7: B¡n k‰nh m°t cƒu nºi ti‚p: r = S Mt https://www svĐnãkhĂccamtcu: p2 + Mt cu ngo⁄i ti‚p tø di»n gƒn •u: R = https://www.facebook.com/tailieupro/ + M°t cƒu ngo⁄i ti‚p tø di»n •u: R = VN VN D fac ebo ok.com/tailieupro/ p 2 + + p 4 v m°t cƒu nºi ti‚p tø di»n gƒn •u: r = a 6 12 https://www facebook com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupr https://www.facebook.com/tailieupr 5:NHNGIUCNNH 6:C CV N V M TTRệ,HNHTRệV VADINU: KHăITRệ: https://www.facebook.com/tailieupr https://www.facebook.com/tailieupr https://www.facebook.com/tailieupr https://www.facebook.com/tailieup https://www.facebook.com/tailieup Truy cập website www.tailieupro.com để nhận thêm nhiều tài liệu H…nh 1: + Thit diằn vuổng gõc trửc l mt ữớng trặn bĂn k‰nh R https://www+Thi‚tdi»nchøatrưclmºt.hfacebook…nhchœnh“tABCDtrong.âcom/tailieupro/AB=2RvAD=h.N‚uthi‚tdi»nqua trưc l mºt h…nh vng th… h = 2R +Thi‚tdi»nsongsongvỵitrưc v https://www d(OO0; (BGHC)) = OM H…nh 2: facebook khổngchứatrửclhnhch com/tailieupro/ nhtBGHCcõkhoÊngcĂchtợitrửc: https://www+NuAB;CDlhaiữớngknh.bĐtfacebookkýtrảnhaiĂycahnhtrử.com/tailieupro/th:V c biằt n‚u AB v CD vuæng gâc th…: VABCD = AB:CD:OO0 + ABCD= AB:CD:OO0:sin(AB;CD) https://www\ \ facebook6.com/tailieupro/ 00 H…nh 3: (AB; OO ) = A AB 0 d(AB; OO ) = O M https://wwwH…nh4:.facebook.com/tailieupro/ H…nh 5: N‚u ABCD l mºt h…nh vng nºi ti‚p h…nh trư th… ÷íng ch†o cıa h…nh vng cơng 2 b‹ng ÷íng ch†o cıa h…nh trư Ngh¾a l : ÷íng ch†o h…nh vuæng = 4R + h https://www VN7:CCVNV facebook HNHNN,KHăINN com/tailieupro/ VNNCệT: https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro https://www.facebook22 com/tailieupro22 H…nh 1: + C¡c cỉng thøc nân cưt: V = h R + Rr + r https://www faceboo k com/tailieupro + N‚uhlchi•ucaocıah…nhnânban ƒuth…tacât¿sŁ:= ; Sxq = l (R + r) ; Stp = R + r + l (R + r) + Thi‚t di»n vuæng gâc tröc c¡ch ¿nh mºt kho£ng x c›t h…nh nân theo mt ữớng trặn cõ bĂn knh + r R https://www.facebook.com/tailieupro + Thi‚t di»n chøa trưc l mºt tam gi¡c c¥n N‚u tam gi¡c â vng c¥n th… h = R N‚u tam gi¡c â l x h tam gi¡c •u th… h = R https://www facebook.com/tailieupro H…nh 2: qua ¿nh m khỉng chøa trưc c›t h…nh nân theo mºt tam gi¡c c¥n SAB: + Thi‚t di»n i + (SO;\(SAB)) = OSM\; ((SAB\);(ABC)) = SM\O https://www facebook com/tailieupr https://www.facebook com/tailieupr + N‚u VN Mltrungi”mcıaABth…AB ? 8: C C V T TH (SMO) TR`N XOAY TRONG KH˘NG GIAN: 2h C¡c cæng thøc chäm cƒu: Sxq = Rh v V = h R ( p döng cho c£ chäm cƒu to) https://www.facebook.com/tailieupr https://www.facebook.com/tailieupr https://www.facebook.com/tailieupr https://www.facebook.com/tailieup C¡c https://www v“tth”sinhratłkhŁitrö: facebook.com/tailieup Truy cập website www.tailieupro.com để nhận thêm nhiều tài liệu https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ https://www.faceb ook.com/tailieupro/ https://www h12 + H…nh n¶m lo⁄i 1: V = https://www com/tailieupro/ +h 2 + KhŁi trö cöt: Sxq = R (h + h2) ; V = R facebook2 3 R tan 3 Rtan H…nh n¶m lo⁄i 2: V = C¡ccỉngthøcli¶nquan‚nparabol facebook com/tailieupro/ b“chaivelip: https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ https://www.facebook.com/tailieupro/ + S htt 4S = parabol p s: Rh x ; 3a Th” t‰ch c¡i phao: V = / /www= = S r facebook.V R 2 parabol=2R hSelip= com/tailieupro/ab https://www.facebook.com/tailieupro/ (R + r)(R r) https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro VN X¡c https://www 9:CCVNCÌBNCÕA ành i”m thỉng qua h» thøc vector: facebook OXYZ: com/tailieupr https://www!!! facebook2(xAxM)3(xBxM).=com/tailieupr0 + Lỵ thuyt cì b£n: 2M A 3M B = th… < (yA yM ) (yB (zA zM ) (zB zM ) = : 2A3B + Tuy nhiảnhttps://wwwmtồaMỡngiÊnhỡn,ta.bĐmfacmĂy:ebo yM ) = vokbĐmCALC.com/tailieuprvnhplnlữổtxA;xB ta ữổc xM T÷ìng tü nh÷ v“y n‚u nh“p yA; yB ta ÷ỉc yM v X¡c ành nh“p zA; zB ta ÷ỉc zM https://wwwtåaºc¡ci”m°cbi»ttrong.facebooktamgi¡c: ( + Tåa º trüc t¥m H l nghi»m cıa h»: https://www.facebook i HABC = 0; HBAC = AC AH=0 com/tailieupr bDB + cDC = !! ! https://www.facebook.com/tailieup ! ! ! + Cho BC = a; AC = b; AB = c ta cõ: ChƠn ữớng phƠn giĂc ngo i E: EB EC ! ! com/tailieupr !!!! !AB; ! ! + Cho BC = a; AC = b; AB = c ta cõ: ChƠn ữớng phƠn giĂc D ca gõc A: + Cho BC = a; AC = b; AB = c ta câ: T¥m nºi ti‚p: aIA + bIB + cIC = = ! ! C¡c ứnghttps://wwwdửngcat chcõhữợng: facebook.com/tailieup Truy cp website www.tailieupro.com nhn thêm nhiều tài liệu = (N‚u 6= l khổng ỗng phflng) !h ! !i + Ba vector çng phflng: a ;b c + BŁn i”m çng !h ! !i phflng: AB; AC AD = (Nu = l khổng ỗng phflng) https://www.facebook.com/tailieupro/ + Th” t‰ch: V ABCD = i AB;! ! AC 00AD 00, di»n t‰ch tam gi¡c: S ! + Th” t‰ch …nh hºp: VABCD:A B https://www.facpebook C D = ABC ! ! h h 2! ! = AB; AC com/tailieupro/ ! i AB; AD AA Chú ỵ: N‚u mºt h…nh hºp chœ nh“t bi‚t di»n t‰ch ba m°t b¶n th… th” t‰ch cıa nâ: V = https://www.faceb S1S2S3 ! +Kho£ngc¡chgiœahai÷íngthflng:d(d1;d2)= ook[u !;u! ]AB ! https://www.faceb j ! [u1 ;u2] j d j ! ud j https://www.facebook com/tailieupro/ !! MŁi quan h» song song v + MŁi quan h» song song: P==P !! + MŁi qua n h» vuæ ng gâ c: P N‚u d P + T÷ìng giao m°t phflng v ) n ? vuæng gâc: ! 0 n = n ; d==d https://www.facebook! P ? ) u ; A; B ! ) n0 ; d d0 P ) m°t cƒu: https://www.facebook.com/tailieupro/ ! ? n ? ? AB ! !? ) = ? ? u0 ; P d !n h !!?)! ! ! = com /ta ilieupro/ i b; 2+ (y + Cho m°t phflng (P ) x0) https://www.facebook.com/tailieupro/ +Trữớng hổp 1: (P ) tip xúc vợi (S) nu d (I; (P )) = R v cıa t¥m I trản mt phflng (P ) +Trữớng hổp 2: ữớng trặn s l trặn thọa mÂn hằ thức: R2 = r2 + [d (I; (P ))]2 + (z y0) â ti‚p i”m s‡ =R z0) h…nh chi‚u vuæng gâc facebook.com/tailieupro/ (P ) c›t m°t cƒu (S) theo mt ữớng trặn giao tuyn d (I; (P )) < R Khi â t¥m h…nh chi‚u vng gâc cıa tƠm I trản mt phflng (P ) ỗng thới bĂn k‰nh r cıa ÷íng https://www facebook com/tailieupro/ T÷ìnggiaíngthflngvm°t cƒu: ÷íng thflng d c›t m°t cƒu t⁄i i”m ph¥n bi»t A v B v ch¿ d (I; (d)) < R + + ! ?) ; MŁi quan h» vuæng gâc cıa c°p vector: ax + by + cz + d = v m°t cƒu (S) : (x https://www (Md) ! u !n ! !u ) 2 ! u = u ; P==d !n ) vợiAd1;Bd2 ook!hu !;AMi +KhoÊngcĂch1imtợiữớngthflng:d(A;d)= com/tailieupro/ com/tailieupro/ https://wwwChúỵ1:HằthứcliảnhằR =1.ABfacebook +[d(I;(d))] com/tailieupro 2 p + Chú ỵ 2: N‚u ABI vng c¥n th… R = 2d (I; (d)) https://www.f acebook.com/tailieupro com/tailieupro + Chú ỵ 3: Nu ABI •u th… R = p d (I; (d)) C¡ch x¡c ành …nh chi‚u vng gâc cıa A tr¶n (P): + https://www facebook Bữợc1:XĂcnhgiĂtr= 222 axA + byA + czA + d CĂc https://www facebook dngtoĂnvãphữỡngtrnh mt chn:GiÊsòmtphflng a+b+c com/tailieupro (P)quaMvctcĂctrửctồa + Bữợc 2: Tồa nh chiu H l H (at + xA; bt + yA; ct + zA) t⁄i A(a; 0; 0); B(0; b; 0); C(0; 0; c) Khi â: + B i to¡n 1: N‚u M l trång t¥m tam gi¡c ABC th…: https://www +B facebook ito¡n2:N‚uMltrüct¥mcıa com/tailieupro ! tamgi¡cABCth… OM=n = 3xM ; = 3yM ; https://www = 3zM !P + B i facebook.com/tailieupr N‚u V + B i to¡n 3: O:ABC th… M l trång t¥m tam gi¡c ABC + + th… M l trüc t¥m tam gi¡c ABC to¡n 4: N‚u 2 OA OB OC +B https://wwwito¡n5:T¥mm°tcƒungo⁄iti‚p.tøfacebookdi»nOABClI ; ; com/B¡nk‰nh:R=t a ilie+b +upr 22 2 2 Chú ỵ vã tam diằn vuổng: Tng bnh phữỡng diằn tch cĂc mt bng bnh phữỡng diằn tch mt https://w ww.facebook.com/tailieupr 2 2 cỈn l⁄i: S +S +S =S OAB OBC OCA ABC https://www.facebookn=[u;[u.com/tailieupr;u]] V N10: C C B I TO N CÜC TRÀ TRONG OXYZ: \ ! 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