初中数学公式

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11ஹḄᕜ=+x2C=a+b
x22ஹḄᕜ=x4C=4a3ஹḄ☢=*S=ab4ஹḄ☢=xS=a.a=a5ஹḄ☢=ஹ-2S=ah+26ஹ!Ḅ☢=ஹS=ah7ஹ"Ḅ☢=#+$x+2S=a+b
h-28ஹ%&='&x2d=2r'&=%&+2r=d+29^ᙊḄᕜ=ᙊᕜ᳛x%&=ᙊᕜ᳛x'&x2c=7rd=27tr10ஹᙊḄ☢=ᙊᕜ᳛x'&x'&*+,ᓫ.ᣚ1ᐗ=101=10ᑖ1ᐗ=100ᑖ23ᓫ.ᣚ145=100616=12ᨴᜧᨴ31ᜩᨵ:1\3\5\7\8\10\12ᨴ;ᨴ30ᜩḄᨵ:4\6\9\11ᨴ62ᨴ28ᜩ<=62ᨴ29ᜩ6ᐰ6365ᜩ<=6ᐰ6366ᜩ1?=24;21;2=60ᑖ1ᑖ=60@1;2=3600@Aᓫ.ᣚ

21CD=1000CᑖD1CᑖD=1000CᔖD1CᑖD=1ᓣ1CᔖD=1Gᓣ1CD=1000ᓣHIᓫ.ᣚ1ᔴ=1000ᓟL1ᓟL=1000L1ᓟL=1MᑭOPᢚᡷS⚪ᑭO=UVWXᡂZᑭO᳛=ᑭO+ᡂZ*100%=UVW+ᡂZ-1
X100%\]^_=Z^X\]`ᑖaᢚᡷ=b▭UW+dUWX100%ᢚᡷVI
ᑭe=Z^Xᑭ᳛X23fgᑭe=Z^Xᑭ᳛h23X1—20%
ijS⚪klḄHI+kᑺḄHI=knḄHIklḄHI+knḄHIX100%=ijknḄHIXij=klḄHI

3klḄHI+ij=knḄHIjᓫ.ᣚ1ᓟD=1000D1D=10ᑖD1ᑖD=10ᔖD1D=100ᔖD1ᔖD=10GD☢ᓫ.ᣚ1ᓟD=100⚕1⚕=10000D1D=100ᑖD1ᑖD=100ᔖD1ᔖD=100GDp⍗S⚪p⍗rs=tjuXp⍗23p⍗23=p⍗rs-tjutju=p⍗rs+p⍗23vwS⚪v+wxyᑖzI{|=}~ᑖzḄᦪᜧvX;v+xyᑖzI{|=}~ᑖzḄᦪᜧwX;w+xyᑖzI{|=}~ᑖzḄᦪS⚪tj=☟tj+tj⌮tj=☟tjXtj☟tj=tj+⌮tj
+2tj=tjX⌮tj
2

4᪛S⚪1ஹr#Ḅ᪛S⚪⌕ᑖ$প᝞ᙠrḄx⌕᪛,ᦪ=ᦪ+1=ᐰ+-1ᐰ=xᦪX1
=ᐰXᦪX1
ফ᝞ᙠrḄX⌕᪛

5(ᡈ;ᦪ+|=ᜧᦪ)¯°S⚪¯°±=tj|X¯°23¯°23=¯°±+tj|tj|=¯°±+¯°23ᦪ³1ஹCᕜS☢aᕜ=x4C=4a☢=xS=axa2ஹV:a:¼⊤☢=¼x¼x6S⊤=2*2*6=¼x¼x¼V=axaxa3ஹCᕜS☢aᕜ=(+)x2C=2(a+b)☢=*S=ab4^V:s:☢a:b:h:প⊤☢(x+x+x)x2S=2(ab+ah+bh)(2)=ஹஹV=abh5ஹs☢ah☢=ஹ+2s=ah+2=☢x24■=☢x2+6ஹ!s☢ah☢=ஹ$=2117ஹ"s☢a#b$h☢=(#+$)x+2s=(a+b)xh+28ᙊS☢CᕜRd=%&r='&পᕜ=%&Ì]1=2*
'&C=nd=2Rr(2)☢='&x'&xf]9ஹᙊÑvh:s☢r☢'&c☢ᕜ(1)Ô☢=☢ᕜ*(2)⊤☢=Ô☢+☢x2(3)=☢x(4)=Ô☢+2x'&10ஹᙊ┵vhs☢r☢'&=☢x+3
ᦪAIᓫ.ᣚ1CD=1000CᑖD<1CᑖD=1000CᔖD<1CᑖD=1ᓣ<1CᔖD=1Gᓣ<1CD=1000ᓣ☢ᓫ.ᣚ1ᓟD=100⚕<1⚕=10000D<1D=100ᑖD1ᑖD=100ᔖD<1ᔖD=100GD

6¦ᦪ+Úᦪ=ᦪ¦ᦪᓝᦪ=Úᦪ2ஹ1¨ᦪx¨ᦪ=¨ᦪÛ¨ᦪ+1¨ᦪ=¨ᦪÛ¨ᦪ+¨ᦪ=1¨ᦪ3ஹtjx23=rsrs+tj=23rs+23=tj4ஹᓫWxᦪI=¦W¦W+ᓫW=ᦪI¦W+ᦪI=ᓫW5ஹÜÝᦔ᳛xÜÝ23=ÜݦIÜݦI+ÜÝᦔ᳛=ÜÝ23ÜݦI+ÜÝ23=ÜÝᦔ᳛6ஹ~ᦪ+~ᦪ=uuXXß~ᦪ=Xß~ᦪ7ஹàáᦪXáᦪ=|àáᦪX|=áᦪ|+áᦪ=àáᦪ8ஹâᦪxâᦪ=+Xßâᦪ=Xßâᦪ9ஹà◀ᦪᓝ◀ᦪ=ᖪà◀ᦪ+ᖪ=◀ᦪᖪx◀ᦪ=à◀ᦪXᦪ¦åæçPâᑖèa2~b2=(a+b)(a-b)a3+b3=(a+b)(a2-ab+b2)a3-b3=(a-b(a2+ab+b2)

7¡é|a+b|WIa|+|b||a-b|W|a|+jb||a|Wb<=>-bWaWbIa-b||a|-|b|-|a|WaW|a|XᐗïysḄè᪷P¥ᦪḄᐵ¥-b+V(b2-4ac)/2a-b-J(b2-4ac)/2aX1+X2=-b/aX1*X2=c/aòóôõᳮᑨøb2-4ac=0òsᨵxßpéḄb᪷b2-4ac>0òsᨵxß¡éḄb᪷b2-4ac<0òsùᨵb᪷<ᨵᐳûüᦪ᪷ýᦪxusin(A+B)=sinAcosB+cosAsinBsin(A-B)=sinAcosB-sinBcosAcos(A+B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1+tanAtanB)ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA)ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA)tan2A=2tanA/(l-tan2A)ctg2A=(ctg2A-l)/2ctgacos2a=cos2a-sin2a=2cos2a-l=l-2sin2asin(A/2)=V((1-cosA)/2)sin(A/2)=-V((l-cosA)/2)cos(A/2)=J((1+cosA)/2)cos(A/2)=-V((l+cosA)/2)tan(A/2)=V((1-cosA)/((1+cosA))tan(A/2)=-V((1-cosA)/((1+cosA))ctg(A/2)=V((1+cosA)/((1-cosA))ctg(A/2)=-V((1+cosA)/((1-cosA))ᓄ2sinAcosB=sin(A+B)+sin(A-B)2cosAsinB=sin(A+B)-sin(A-B)2cosAcosB=cos(A+B)-sin(A-B)-2sinAsinB=cos(A+B)-cos(A-B)sinA+sinB=2sin((A+B)/2)cos((A-B)/2cosA+cosB=2cos((A+B)/2)sin((A-B)/2)tanA+tanB=sin(A+B)/cosAcosBtanA-tanB=sin(A-B)/cosAcosB

8ctgA+ctgBsin(A+B)/sinAsinB-ctgA+ctgBsin(A+B)/sinAsinBᦪᑡ#n⚗1+2+3+4+5+6+7+8+9+*,,+n=n(n+1)/21+3+5+7+9+1l+13+15+-"+(2n-l)=n22+4+6+8+10+12+14+…+(2n)=n(n+1)12+22+32+42+52+62+72+82+…+n2=n(n+1)(2n+l)/613+23+33+43+53+63+…n3=n2(n+1)2/4l*2+2*3+3*4+4*5+5*6+6*7+…+n(n+l)=n(n+l)(n+2)/3ᐸ&'ᵨᦪ)*+,ᳮa/sinA=b/sinB=c/sinC=2R./ᐸ0R⊤234Ḅ᜜7ᙊ9:+,ᳮb2=a2+c2-2accosB./B;0GᱥI᪗?@Ay2=2pxy2=-2pxx2=2pyx2=-2pyJKLM☢S=c*hOKLM☢S=c'*h*K┵M☢S=l/2c*h'*KQM☢S=l/2(c+c')h'ᙊQM☢S=l/2(c+c,)l=pi(R+r)1ᳫḄ⊤☢S=4pi*r2ᙊLM☢S=c*h=2pi*hᙊ┵M☢S=l/2*c*l=pi*r*lSTl=a*ra;ᙊCḄSUᦪr>0ᡧ4☢s=l/2*l*r┵WWV=1/3*S*Hᙊ┵WWV=l/3*pi*r2hOKLWV=S'L./ᐸ0,S';JY☢☢ZL;MKTLWWV=s*hᙊLWV=pi*r2h[Eᦪ)/\]^ᦪ)_`abcdᑖfa2-b2=(a+b)(a-b)a3+b3=(a+b)(a2-ab+b2)a3-b3=(a-b(a2+ab+b2)3ghla+bl<|a|+|b||a-bl<|a|+|b||a|-b|a|-lbl-lal

9ᑨrb2-4ac=0./@AᨵtuvhḄw᪷b2-4ac>0./@AᨵtughḄw᪷b2-4acv0./@Axᨵw᪷Zᨵᐳ᪋{ᦪ᪷3|ᦪtsin(A+B)=sinAcosB+cosAsinBsin(A-B)=sinAcosB-sinBcosAcos(A+B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(l+tanAtanB)ctg(A+B)=(ctgActgB-1)Z(ctgB+ctgA)ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA)tan2A=2tanA/(1-tan2A)ctg2A=(ctg2A-1)/2ctgacos2a=cos2a-sin2a=2cos2a-1=l-2sin2asin(A/2)=A/((1-cosA)/2)sin(A/2)=-A/((1-cosA)/2)COS(A/2)=A/((1+cosA)ফcos(A/2)=«((1+cosA)/2)tan(A/2)=A/((1-cosA)/((1+cosA))tan(A/2)=-A/((1-cosA)/((1+cosA))ctg(A/2)=V((1+cosA)/((1-cosA))ctg(A/2)=-*V((1+cosA)/((1-cosA))ᓄ2sinAcosB=sin(A+B)+sin(A-B)2cosAsinB=sin(A+B)-sin(A-B)2cosAcosB=cos(A+B)-sin(A-B)-2sinAsinB=cos(A+B)-cos(A-B)sinA+sinB=2sin((A+B)/2)cos((A-B)/2cosA+cosB=2cos((A+B)/2)sin((A-B)/2)tanA+tanB=sin(A+B)/cosAcosBtanA-tanB=sin(A-B)/cosAcosB

10ctgA+ctgBsin(A+B)/sinAsinB-ctgA+ctgBsin(A+B)/sinAsinBᦪᑡ#n⚗1+2+3+4+5+64-7+8+9+…+n=n(n+1)/21+3+5+7+9+1l+13+l5+...+(2n-l)=n22+4+6+8+10+12+14+…+(2n)=n(n+1)12+22+32+42+52+62+72+82+…+n2=n(n+l)(2n+1)/613+23+33+43+53+63+…n3=n2(n+1)2/41*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+l)(n+2)/3ᐸ&'ᵨᦪ)*+,ᳮa/sinA=b/sinB=c/sinC=2R./ᐸ0R⊤234Ḅ᜜7ᙊ9:+,ᳮb2=a2+c2-2accosB./B;0GᱥI᪗?@Ay2=2pxy2=-2pxx2=2pyx2=-2pyJKLM☢S=c*hOKLM☢S=d*h*K┵M☢S=l/2c*H*KQM☢S=l/2(c+c')h'ᙊQM☢S=l/2(c+c')l=pi(R+r)lᳫḄ⊤☢S=4pi*r2ᙊLM☢S=c*h=2pi*hᙊ┵M☢S=l/2*c*l=pi*r*lSTl=a*ra;ᙊCḄSUᦪr>0ᡧ4☢s=l/2*l*r┵WWV=1/3*S*Hᙊ┵WWV=l/3*pi*r2hOKLWV=SL./ᐸ0S;JY☢☢ZL;MKTLWWV=s*hᙊLWV=pi*r2h☢ᓫᣚ1@ᓟ=100⚕Z1⚕=10000@Z1@=100@ᑖ1@ᑖ=100@ᔖZ1@=100@1=1

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32PQ3Mᐗ;=Ḅ"RSḄᦪXஹyḄ;L"CDTAMᐗ;=Ḅ;A'UV;AMᐗ;=WᨵX▲ZA'[\5᝞^Mᐗ;=_`a5bc32LdLḄ'eAὶᔠᙠ;hLᡂ;A᦮jCDὶk_CLᵫeA;=L0?ᨵAᦪḄLᡂ5Mᐗ;=LPQmnoLpq;AḄᦪḄᦪLLCDLḄ'33Mᐗ;=LḄ'(rLḄ'ḄsCD'LtMᐗuᓄ5;ᐗr'a5vᐗ(CDwxvᐗ(7awx(yLz{LX'34|ᐗ;=L}ᐸ'(?ᨵ|AᦪḄ|ᐗ;=L4'ᵨ⚪5;ᐗ;=bS9L51;ᐗ;=9ᙠ?ᨵᦪḄbS9p᝞>?ᨵ;AᦪஹᑖIb?ᦪ0BᦪḄ=ᦪ;=T᪵ḄbS9CD;ᐗ;=b[

33S9PQ3bS9ᡂkḄᦪḄ"a5TAbS9Ḅ'ᡠᨵT᪵Ḅ'Ḅᔠ7a5TAbS9Ḅ'rbS9Ḅ'ḄsCD'bS952;ᐗ;=bS9Ḅ'(53;ᐗ;=bS9LᵫeA?ᨵ;AᦪḄ;=bS9LᡂḄbS9LCD;ᐗ;=bS9bS9LpqAbS9Ḅ'ḄᐳᑖCDTAbS9LḄ'54;ᐗ;=bS9LḄ'(';ᐗ;=bS9LḄ;E*+,1ᐜr:bS9LᔜAbS9Ḅ'K2ᙠr:TbS9Ḅ'ḄᐳᑖᑮTAbS9LḄ'pὃᦪᦪ9ஹcᳮ|,|;ᐗM=1d᪷11☢d1
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35(1)`ÊᦪḄqA\ᦪḄᢣᦪW±2;(2)`Êᦪb?ᨵÍIᡃÏÐᔠTAᩩÒḄ᪷CDᨬ7᪷23´µ᪷Ḅwஹx³´᝞eA᪷ᓄᡂᨬ7᪷Ó`ÊᦪRTeA᪷CD1᪷3;ᐗM=}ᐸ'(31;ᐔM=>?ᨵ;AᦪBᦪḄᨬÔ=ᦪ2ḄCD;ᐗM=32ᱯÖḄ;ᐗM=Ḅ'(33;EḄ;ᐗM=Ḅ'(;;×(ᵨ×(';ᐗM=Ḅ;E*+,1ᓄM=⚗ᦪ51ᵨM=⚗ᦪ-◀Øᓄ5ᨌ2+px+q=0Ḅ892⚗Gᦪ⚗ÝÞØᓄ5-2+px=-qḄ893×mw$“;=⚗ᦪ;àḄ”áᡂ5?ᨵᦪḄâᐰ89Þ;AGᦪ4ᨵ᪷Ḅcäå(1)ær/2/4-qு0myᨵA®ᦪ᪷K(2)æ/2/4-q=0,yᨵARSḄ®ᦪ᪷(Mè᪷)K

36(3)æ/2/4-qீ0,yX®᪷34;ᐗM=Ḅr᪷9;ᐗM=ax"2+bx+c=0(a!=0)Ḅr᪷9,æí2-42஺>=0mxl,2=(-b(+,-)sqrt(b2-4ac))/2a35;ᐗM=᪷Ḅᑨò9ax"2+bx+c=0(a!=0)ædelta=b-2-4ac>0mᨵAbRSḄ®ᦪ᪷Kædelta=b-2-4ac=0mᨵARSḄ®ᦪ᪷Kædelta=b"2-4ac<0Elt,¬ᨵ®ᦪ᪷36;ᐗM=Ḅ᪷dᦪḄᐵAᦪxl,x25᪷Ḅ;ᐗM=(M=⚗ᦪ51)/2-(xl+x2)x+xl?x2=04'ᵨ⚪pὃᦪᦪ9ஹcᳮ(ù),ùZ⚗9Ḅùᑣ³´1ᓫ⚗9dZ⚗9û?ᨵ;ᦪÍIḄ((ᒹ.)³´Ḅ9ÈCDᓫ⚗9ᓫýḄ;AᦪᡈÍI_ᓫ⚗9ᓫ⚗9pḄᦪÍ\ᦪCDTAᓫ⚗9(ᡈÍI\ᦪ)ḄᦪÍᦪ7aᦪ

37æ;Aᓫ⚗9Ḅᦪ1ᡈTm“1”ÇGḕᶍ
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$Ḅ⚗0ᦪ⚗ᓫ⚗<=>?4⚗ḄᱯAB-ᓫ⚗ḄᦪCᡈEFᓫ⚗ḄḄGHᢣᦪ
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38ឋx1᝞f(x)==g(x),*+deVᦪUa,1ᨵf(a)=g(a)ឋx2᝞f(x)==g(x),*+f4⚗Ḅ-⚗ᦪ,ydzc15ᐗ4⚗Ḅ᪷}ᙢ4⚗f(x)ḄUce0ḄJKᦪxḄU4⚗f(x)Ḅ᪷24⚗ḄCஹEG214⚗ḄCஹE224⚗ḄGᓫ⚗Gᵨᦪ?QḄᦪdeḄᑣ]Ḅᢣᦪ?QḄ34⚗ḄG4⚗4⚗Gᐜᵨ4⚗c;⚗G=4⚗Ḅᔜ⚗BᡠqḄC230ᵨGIH(a+b)(a-b)=a"2-b2fᦪḄfᦪḄḄcefᦪḄHHᐰH(a+b)-2=a-2+2ab+b-2

39(a-b)2=a2-2ab+b~2fᦪᡈfᡈḄHceḄHCᡈEḄ23ᓫ⚗Ḅ◀fᓫ⚗◀,ḄᦪஹᦪḄᑖ)◀Fde*!ᙠ¡◀:¢£Ḅ]Ḅᢣᦪ_?QᖪḄde!ᙠ◀:¢£Ḅ]ḄᢣᦪḄ¥ᦪ_?QᖪḄ4⚗ᜐ=ᓫ⚗ᐜB4⚗Ḅ;⚗◀=ᓫ⚗BᡠqḄᖪCὃᦪ¨6ᦪஹyᳮª«¬®¬¯ᑖ°1ᑖ°11᝞ᦪ
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42ὃᦪ¨6ᦪஹyᳮª«ê®ê¯ÅᐗÅH»71ÅᐗÅH»ÅᐗÅH»711ÅᐗÅH»$ᨵfJKᦪ%&JKᦪᨬSᦪ2Ḅ᦮H»/QÅᐗÅH»ᐵex,yḄÅᐗÅH»Ḅ}ºax2+bxy+cy2+dy+ey+f=0ᐸax2,bxy,cy2H»ḄÅ⚗d,e⚗f0ᦪ⚗12ÅᐗÅH»72ÅᐗÅH»7Ḅ°21®×-ðḄÅᐗÅH»7Ḅ°mÅᐗÅH»7ḄÅᐗÅH»<ᑖ°ᡂfH»Ḅp᎛ᡃ,<=Bᑖ°qᑮḄᔜH»ôH»7ḄH»77ᡂfõḄH»7ᩭ°×°H»7ḄH/Qᑖ°ö22®Å×-ðḄÅᐗÅH»7Ḅ°ὃᦪ¨6ᦪஹyᳮª«÷®÷¯Åøᦪ1ÅøᦪÃᐸùú11ÅøᦪᡃBøᦪy=ax?+bx+ca,b,cQ0ᦪ&a
ce0Åøᦪ12øᦪy=ax2a
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43ᵨ⊤:ᔜ7dzU?QýḄᙶ᪗
ᯠᵨᐝḄὶᩭᑮᦪy=x2Ḅ!"#$%ᱥᦪy=x2Ḅ'()*+%ᱥy=x2!ᩩ%ᱥ-ᐵ/y0ᡂ2*Ḅᡃy0#$%ᱥy=x2Ḅ2*02*04%ᱥḄᯖ#$%ᱥḄ⚔13ᦪy=ax2+bx+c>a?@/0BḄ'4ឋD%ᱥy=ax?+bx+cḄ⚔ᙶ᪗->-b/2a,4ac-b2/4aB,2*0LM-x=-b/2a,Naு0P%ᱥḄQRᔣTUVᔣTW▲YZ[Naீ0P%ᱥḄQRᔣ]UVᔣ]W▲YZNaு0P^ᦪy=ax?+bx+cᙠxீ-”2aP-⌴bḄᙠxு-b/2aP-⌴cḄ;ᙠx=-b/2aᜐfyᨬh=4ac-b2/4aNaீ0P^ᦪy=ax2+bx+cᙠx>-b/2aP-⌴bḄ[ᙠx=-?/2aᜐfyᨬᜧ=4ac-b2/4a2᪷klmᩩno^ᦪ21᪷klmᩩnpq^ᦪ22^ᦪḄᨬᜧrᡈᨬhr23tᐗ^LMḄ'vwxὃᦪz{ᦪ|}ஹqᳮ>Bᦪ'1ᦪ011ᨵᔣᙠzᢈ4x+tᩩḄ"?Lᔣ(

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4813#ᦪy=ax2+bx+caJK.0Ḅ2ឋPÆᱥ4y=ax?+bx+cḄ⚔ᙶ᪗I-b/2a,4ac-b2/4a,&+8Ix=-b/2a,aு0Æᱥ4Ḅ*Îᔣϳᔣb▲ÐÑ]aீ0Æᱥ4Ḅ*ÎᔣMϳᔣMb▲ÐÑaு0k#ᦪy=ax?+bx+cᙠxீ-”2aI⌴Ḅᙠxு-b/2aI⌴Ḅ;ᙠx=-b/2aᜐzÅyᨬ=4ac-b?/4aaீ0,k#ᦪy=ax2+bx+cᙠx-b/2aI⌴Ḅ]ᙠx=-J/2aᜐzÅyᨬᜧ=4ac-b2/4a2᪷?×ØᩩÙ¡k#ᦪ21᪷?×ØᩩÙ}wk#ᦪ22k#ᦪḄᨬᜧᡈᨬ23ᐗk8Ḅ¢¦ὃᦪ¨Û{ª«ஹwᳮ®1Tᨵ³Üᨵᩩ342T~Ý4Þᨬß3à<ᡈK<Ḅ⊡<âK4à<ᡈK<Ḅã<âK5ᨵ³Üᨵᩩ342×Ø34ᚖ3634᜜634ᔜç,Ḅᡠᨵ4Þ¦ᚖ4Þᨬß7蹪ᳮ34᜜ᨵ³Üᨵᩩ346ᩩ34è¹

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ᨬᐳ
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