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

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Truy cập website www.tailieupro.com để nhận thêm nhiều tài liệu hơn 1

TUY N T P C˘NG THÙC GI I NHANH TR C NGHI M TO N

S:ABC

6

1

https://www.facebook \ com/tailieupro/

Cæng thøc 2: V ABCD = 6AB:CD:d (AB; CD) sin AB; CD

Cæng thøc 3: V SABC = 2S1S2sin (Cæng thøc th” t‰ch gâc nhà di»n)

Cæng thøc 4: Th” t‰ch tø di»n •u V ABCD = 12 p

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12

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https://www.facebook.com/tailieupro/

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).

Gâc lo⁄i 3: (SK; (SDE)) = KSG (Gâc giœa ÷íng cao SK v m°t b¶n (SDE))

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https://www.facebook.com/tailieupro

Gâc lo⁄i 1: ((SAB); (P )) = SCD (Gâc giœa m°t b¶n v m°t phflng ¡y).

https://www\[.facebook.com/tailieupr

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).

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https://www.facebook.com/tailieupr https://www.facebook.com/tailieupr

https://www.facebook.com/tailieup https://www.facebook.com/tailieup

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M°t cƒu lo⁄i 2: N‚u SA vuæng gâc vîi ¡y th…: R2 = R D2 + C¡c v§n • cƒn chó þ v• R D :

4

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+ N‚u ¡y l tam gi¡c vuæng th… RD = 1 c⁄nh huy•n v n‚u ¡y l tam gi¡c •u th… RD =

p

https://www+ N‚u ¡y l h…nh chœ nh“t th… R+N‚u¡yl…nhvuængth…RD = D =.af212acebook..com/tailieupro/

2 ÷íng ch†o.

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M°t cƒu lo⁄i 3: N‚u O:ABC l tam di»n vuæng t⁄i O th… R 2 = 14(OA 2 + OB 2 + OC 2 ).

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+https://wwwN‚u¡yltamgi¡cvuængth…Ol.trungfacebooki”mc⁄nhhuy•n..com/tailieupro/ + 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.

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M°t cƒu lo⁄i 6: Châp S:ABC tŒng qu¡t câ chi•u cao SH v t¥m ¡y l O th… ta gi£i ph÷ìng tr…nh:

(SHhttps://wwwx) 2 +OH 2 =x 2 +R 2 ”…mx.Vîifacebookxt…m÷æctacâR 2 =x 2.+com/tailieupro/R 2

p 4

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V Nhttps://www5:NHÚNGIUCNNH˛.facebookVADINU:.com/tailieupro

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Truy cập website www.tailieupro.com để nhận thêm nhiều tài liệu hơn 3 H…nh 1:

https://www+Thi‚tdi»nchøatröclmºt.hfacebook…nhchœnh“tABCDtrong.âcom/tailieupro/AB=2RvAD=h.N‚uthi‚tdi»nqua tröc l mºt h…nh vuæng th… h = 2R

https://www+Thi‚tdi»nsongsongvîitröc.vfacebookkhængchøatröclh…nhchœ.com/tailieupro/nh“tBGHCcâkho£ngc¡chtîitröc:

d(OO0; (BGHC)) = OM

H…nh 2:

https://www+N‚uAB;CDlhai÷íngk‰nh.b§tfacebookkýtr¶nhai¡ycıah…nhtrö.com/tailieupro/th…:V ABCD =1AB:CD:OO 0 :sin(AB;CD).

6

+ °c bi»t n‚u AB v CD vuæng gâc nhau th…: V ABCD = 1AB:CD:OO 0

https://www\ 0 \ 0.facebook6.com/tailieupro/

H…nh 3: (AB; OO ) = A AB

d(AB; OO 0 ) = O 0 M.

https://wwwH…nh4:.facebook.com/tailieupro/ H…nh 5: N‚u ABCD l mºt h…nh vuæng nºi ti‚p trong h…nh trö th… ÷íng ch†o cıa h…nh vuæng công 2 2

b‹ng ÷íng ch†o cıa h…nh trö Ngh¾a l : ÷íng ch†o h…nh vuæng = 4R + h

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+ C¡c cæng thøc nân cöt: V = 3 h R + Rr + r ; S xq = l (R + r) ; S tp = R + r + l (R + r)

+ https://www

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+ Thi‚t di»n vuæng gâc tröc c¡ch ¿nh mºt kho£ng x c›t h…nh nân theo mºt ÷íng trÆn câ b¡n k‰nh .

+ https://www.facebook.com/tailieupro

+ Thi‚t di»n chøa tröc l mºt tam gi¡c c¥n

N‚u tam gi¡c â vuæng c¥n th… h = R N‚u tam gi¡c â l tam gi¡c •u th… h = R 3

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+ (SO;\(SAB)) = OSM\; ((SAB\);(ABC)) = SM\O.

+ N‚uhttps://wwwMltrungi”mcıaABth…AB.?facebook(SMO)..com/tailieupr

V N 8: C C V T TH TR`N XOAY TRONG KH˘NG GIAN:

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https://www.facebook.com/tailieup C¡c https://wwwv“tth”sinhratłkhŁitrö:.facebook.com/tailieup

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https://www.facebh12ook.com/tailieupro/

+ KhŁi trö cöt: S xq = R (h1 + h2) ; V = R2.

+ h

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H…nh n¶m lo⁄i 1: V = R tan H…nh n¶m lo⁄i 2: V = Rtan

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2

Th” t‰ch c¡i phao: V = 4 (R + r)(R r)2

https://www.facebook.com/tailieupro https://www.facebook.com/tailieupro

X¡c ành i”m thæng qua h» thøc vector:

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: 2 (z A z M ) 3 (z B z M ) = 0

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AC AH=0

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+ Cho BC = a; AC = b; AB = c ta câ: Ch¥n ÷íng ph¥n gi¡c trong D cıa gâc A: !! !

+ Cho BC = a; AC = b; AB = c ta câ: Ch¥n ÷íng ph¥n gi¡c ngo i E:!EB !EC aIA + bIB + cIC = 0 !

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Truy cập website www.tailieupro.com để nhận thêm nhiều tài liệu hơn 5 + Ba vector çng phflng:!h

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+ Th” t‰ch: V

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MŁi quan h» song song v vuæng gâc:

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+ MŁi quan h» vuæng gâc: P P 0 !n n0; d d0 !u

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N‚u d P ) n ? u ; A; B P ) !n ? AB.

+ T÷ìng giao m°t phflng v m°t cƒu: ! !

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ax + by + cz + d = 0 v m°t cƒu (S) : (x 2+ (y 2 + (z 2 = R2

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trÆn thäa m¢n h» thøc: R 2 = r 2 + [d (I; (P ))] 2

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https://www.f 3 acebook.com/tailieupro

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C¡ch x¡c ành …nh chi‚u vuæng gâc cıa A tr¶n (P):

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t⁄i A(a; 0; 0); B(0; b; 0); C(0; 0; c) Khi â:

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B i to¡n 6: Vi‚t d n‹m trong (P ) v qua A sao cho d(M; d) lîn nh§t: u = n ;AM

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Trang 9

8 Truy cập website www.tailieupro.com để nhận thêm nhiều tài liệu hơn

+ Tam gi¡c ABC vuæng c¥n khi tan 450 = 2a , =1.

https://www0 .pf acebookp 3.com/tailieupro/

+ Tam gi¡c ABC •u khi tan 30 = a2 , a = 3.

https://www.facebo 3 ok.com/tailieupro/

+ Tam gi¡c ABC câ gâc 1200 khi tan 600 = a2 , =p3

+https://www.facebook.com/tailieupro/

+ Tam gi¡c ABC câ di»n t‰ch l S khi S = 2 p , = p5 S 2

B¡n k‰nh ÷íng trÆn ngo⁄i ti‚p R = abc , b¡n k‰nh ÷íng trÆn nºi ti‚p: r = 2S .

a + b + c

4S

https://wwwçthàmsŁc›ttröchonht⁄ibŁn.facebooki”mcâhonhºl“pthnh.c§pcom/tailieupro/sŁcºngn‚u9b 2 =100ac.

çhttps://wwwthàmsŁc›ttröcho2nht⁄othnh.bafacebook.com/tailieupromi•ndi»nt‰chcâdi»nt‰chphƒntr¶nvdi»nt‰chphƒnd÷îi b‹ng nhau khi v ch¿ khi 5b = 36ac.

cx++d

H mhttps://wwwsŁçngbi‚ntr¶nDn‚uadbc>.0;fad 2=cebookDvnghàchbi‚ntr¶n.Dcom/tan‚uadbc<0;idlieupro2=D.

Ti‚p tuy‚n vîi ti»m c“n:

+ Ti‚p tuy‚nhttps://wwwt⁄iMc›tc¡cti»mc“nt⁄iAv.Bfacebookth…Mltrungi”mcıaAB.com/tailieup + Kho£ng c¡ch tł M tîi TC : 1 jcx + dj.

https://wwwjcjM.facebook.com/tailieup

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+ Kho£ng c¡ch tł M tîi TCN: jad bcj 1

jcj jcx M

+IA= jad bcj 2 v IB = 2 jcx + d vîi I l giao 2 ti»m c“n

2

°c bi»t chó þ: i”m M thäa m¢n mºt trong c¡c y‚u tŁ: TŒng kho£ng c¡ch ⁄t gi¡ trà nhä nh§t/Chu

https://wwwvitamgi¡cIABnhänh§t/B¡nk‰nh.facebook÷íngtrÆnnºiti‚ptamgi¡c.com/tailieupro/IABlînnh§t/Kho0£ngc¡chtłItîiti‚p tuy‚n ⁄t gi¡ trà lîn nh§t

th… i”m M â ph£i thäa m¢n t‰nh ch§t: IA = IB , jy (x M )j = 1.

C¡ch nh“n di»n ç thà h m ph¥n thøc b“c nh§t tr¶n b“c nh§t:

+https://wwwTi»mc“nngang:y=a.N‚uti»m.c“nfacebookngangn‹mtr¶nOxth…ac.>com/tailieupro0cÆnn‚un‹md÷îith…ac<0

cd

+ Giao Oy y = d N‚u giao i”m n y n‹m tr¶n Ox th… bd > 0 cÆn n‚u n‹m d÷îi th… bd < 0

+https:GiaoOxx=/b /wwwN‚ugiaoi”mn.yfacebookn‹mb¶ntr¡iOyth…ab>0.cÆncom/tailieupron‚ub¶nph£ith…ab<0

a

Vhttps://wwwN16:˙THÀHMS¨LÔY.facebookTHØA,MÔVLOGARIT:.com/tailieupro

Lo⁄i 1: ç thà m sŁ mô:

+ Thø tü: 0 < b < a < 1 < d < c (Mµo: Giao 4 ç thà vîi ÷íng thflng x = 1 ” ¡nh gi¡ nhanh nh§t!).

+ H mhttps://wwwsŁy=axcât“px¡cànhD=R,.t“pfacebookgi¡tràE=(0;+1)..com/tailieup

+ ç thà h m sŁ y = ax luæn i qua i”m I(0; 1) v câ ti»m c“n ngang l tröc ho nh Ox.

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