初中公式大全（Formula of junior high school）

初中公式(Formulaofjuniorhighschool)

Thephysicalquantityiscalculatedbytheformula

Nu=S/tIm/S=3.6Km/h

Soundvelocitynu=340m/s

Thespeedof1ightCisequalto3times108meterspersecond

Densityrho=m/V1g/cm3=103Kg/m3

ResultantF=Fl-F2

F=Fl+F2FlandF2areonthesamelineandinopposite

directions

FlandF2areonthesamelineandinthesamedirection

PressurepisequaltoFoverS

P=rhoghp=F/Sisapplicabletosolid,liquidandgas

P=rhoghappliedtotheverticalsolidcolumn

P=rhoghcandirectlycalculatetheliquidpressure

1standardatmosphericpressure=76cmHgcolumn=1.01x105

Pa=10.3mwatercolumn

Buoyancy=G-F

Floatingandlevitating:Ffloat=G

Ffloat=Grow=rhoGVrow

Todeterminewhethertheobjectisbuoyantbybuoyancy

(2)judgeobjectsaccordingtotheconditionsofobjects

Whatstate

(3)findtheproperformulatocalculatebuoyancy

Object'sbuoyancycondition(premises:theobjectisimmersed

in1iquidandonlybybuoyancyandgravity):

Ffloat>G(rholiquid>rho)floattofloat.Ffloat=G(rho

liquid=rho)suspension

Ffloat<G(rho)sinks

LeverageequilibriumconditionFlLI=F2L2leverage

equilibriumconditionisalsocalledleverageprinciple

ThepulleygroupF=G/n

F=(Gmoving+G)/n

SF=nSGidealpulleyblock

Ignorethefrictionbetweentheshafts

N:thenumberofstrandsonthemovablepulley

WorkW=F,S=Pt1J=IN?M=1w?s.

PowerP=W/t=Fnu1kw=103W,1mw=103KW

W=Gh(verticallift)=FS(horizontalmovement)=Wtotal

-W=etaW

TheextraworkWisequaltoWtotal-WisequaltoGmotion

h(ignoringtheinteraxialfriction)=fL(incline)

TotalworkW=Wuseful+W=FS=Wuseful/eta

Themechanicalefficiencyeta=Wisuseful/Wtotal

EtaisequaltoGovern,F.

=Gobject/Gobject+Gactiondefinition

Applicabletomovablepulley,pulleyblock

TheformulaeofphysicsinChinese

Characteristicorprincipleseriescircuitparallelcircuit

Time:tt=tl=t2t=tl=t2

I=I=I=I=I=I=I=I=I=I=I=I=I=I=I=I

=I=I=I=I=I=I=I=I=

U=U1=U1=U2

Chargequantity:QpowerQ=Qpower1=Qpower2Qelectricity

=Qpower1+Qpower2

Resistance:RR=R1=R21/R=1/RI+1/R2[R=RIR2

/(RI+R2)]

Electricwork:WW=W1+W2W=W1+W2

Power:PP=P1+P2P=P1+P2

Electricheat:QheatQhot=Qhot1+Qhot2Qhot=Qhot

1+Qheat2

Thedeformationoftheformulaoftheequationofphysical

quantity(unit)

V(m/S)V=S:distance/t:time

TheforceofgravityG

(N)G=mgm:mass

G:9.8N/kgorlON/kg

Thedensityofrho

(kg/m3)rho=

M:quality

V:volume

ResultantforceFor

(N)thesamedirection:F=Fl+F2

Intheoppositedirection:F=Fl-F2intheoppositedirection,

Fl>F2

BuoyancyFfloating

(N)Ffloat=G-G-G-G-G-G-G:thegravityofanobject

inaliquid

BuoyancyFfloating

(N)Ffloat=Gobjectthisformulaonlyapplies

Objectsfloatorfloat

BuoyancyFfloating

(N)Ffloat=Grow=mrowG=rholiquidgVrowGrow:the

gravityoftheliquid

Rowm:thequalityoftheliquid

Rholiquid:densityofliquid

V:thevolumeoftheliquid

(thatis,thevolumeintheliquid)

LeveragebalanceconditionFILI=F2L2Fl:dynamicLI:power

arm

F2:resistanceL2:resistancearm

ThepulleyF=G

S=hF:thepullofthefreeendoftherope

G:thegravityoftheobject

S:thedistancefromthefreeendoftherope

H:thedistancethattheobjectrises

F=(Gobject+Gwheel)

S=2hGobjects:gravityoftheobject

Gwheel:thegravityofthepulley

PulleygroupF=(Gobject+Gwheel)

S=nhn:byusingthenumberofpulleyrope

MechanicalworkW

(J)W=FsF:force

S:thedistancetraveledinthedirectionoftheforce

Andthereisalotofwork

TotalworkWisequaltoGobjecth

WisequaltoFsforverticalplacementofslides

Mechanicalefficiencyeta=x100%

PowerP

(w)P=

W:work

T:time

Thepressurep

(Pa)P=

F:stress

S:forcearea

Liquidpressurep

(Pa)P=rhoghrho:densityofliquid

H:depth(fromliquidleveltorequestpoint

Verticaldistance

HeatQ

(J)Q=cmdeltatc:thespecificheatcapacityofmatter:mass

Deltat:thechangeintemperature

Combustionoffuel

Q(J)Q=mqm:mass

Q:calorificvalue

Commonphysicalformulasandimportantknowledgepoints

One.Thephysicalformula

Theformulaoftheformulaisdeformed

Seriescircuit

CurrentI(A)I=Il=12=...Thecurrentisequaleverywhere

Seriescircuit

VoltageU(V)U=UI+U2+...Seriescircuit

Thepartialpressureeffect

Seriescircuit

TheresistanceR(Q)R=RI+R2+...

Parallelcircuit

CurrentI(A)I=Il+12+...Thedrycurrentisequaltoeach

Thesumofthebranchcurrent(shunt)

Parallelcircuit

VoltageU(V)U=UI=U2=...

Parallelcircuit

TheresistanceR(Q)=++...

Ohm，slawI=

Thecurrentandvoltageinthecircuit

It'sproportional,inverselyproportionaltotheresistance

CurrentdefinitionI=

Q:charge(coulomb)

T:time(S)

ElectricworkW

(J)W=PtU:voltageI:current

T:timeP:power

PowerP=I2R=U2/RU:voltageI:current

R:resistance

Electromagneticwavevelocityandwave

Long,frequencyrelationshipC=lambdanuC:wavevelocity(the

wavevelocityoftheelectromagneticwaveisconstant,equal

to3times108m/s)

Lambda:wavelengthnu:frequency

2.Knowledgepoints

1.Severalvaluestoremember:

Thespeedoftransmissionofsoundintheair:340m/sblight

propagatinginavacuumorair:3x108m/s

C.thedensityofwater:1.0x103kg/m3d.theheatcapacity

ofthewater:4.2x103j/(kg?℃)

E.Voltageofadrycell:1.5vf.Voltageofthehomecircuit:

220V

G.Safetyvoltage:nomorethan36V

2.Density,specificheatcapacity,heatvaluearethe

propertiesofmatter,andthevaluesofthesamesubstancesare

generallyunchanged.

Forexample,aglassofwaterandabucketofwater,their

densityisthesame,thespecificheatcapacityisthesame,

Theimageofaflatmirrorissimilartoanobject'ssymmetry.

Soundcannotbetransmittedinavacuum,andlightcanspread

inavacuum.

4.Ultrasonicfrequency:frequencyabove2000sounds,for

example:bats,ultrasonicradar;

5.Infrasound:volcaniceruption,earthquake,windexplosion,

tsunami,etc.Canproducetheinfrasound,nuclearexplosion,

missilelaunch,etc.

6.Lighttravelsinstraightlinesinthesamehomogeneous

medium.Shadow,smallholeimaging,solareclipse,theeclipse

isallalongthestraightline.

Whenlightisrefracted,itisalwaysslightlylargerinthe

air.Lookatthethingsinthewaterandseetheshallowimage.

8.Theconvexlensconvergestothelightandtheconcavelens

divergesfromthelight.

9.Thelawofconvexlensimaging:theobjectisreducedand

invertedbyadoublefocallength.Betweentwofocallengthand

onefocallength,itisinvertedandenlarged.Ina1timesfocal

length,it'sapositive,magnifiedimage.

10.Theslidingfrictionsizeisrelatedtotheroughnessof

thepressureandthesurface.Therollingfrictionissmaller

thantheslidingfriction.

11.Pressureisthephysicalquantityoftheeffectofpressure,

andtheeffectofpressureisrelatedtothesizeandforcearea

ofthepressure.

Whenthevoltageisdelivered,highvoltagetransmissionis

applied.Thereason:youcanreducethelossofpoweronthe

transmissionline.

13.Principleofelectricmotor:theforceoftheelectriccoil

inthemagneticfieldturns.Energyisconvertedinto

mechanicalenergy.

14.Principleofgenerator:electromagneticinduction

phenomenon.Mechanicalenergyisconvertedintoelectricity.

Microphone,transformeristheprincipleofelectromagnetic

induction.

Opticalfiberisthemediumoflighttransmission.

16.ThemagneticinductionlineisemittedfromtheNpoleof

themagnetandfinallyreturnstotheSpole

Theformulaofmiddleschoolmathematics:theformulaofcircle

andarc:theauthorofthearticle:purplehan2013-03-13

14:13:09

IsnsideofeachinteriorAngleisequalto(n-2)x180°

/n

Arclengthcalculationformula:L=n-R/180

Fanareaformula:Sfan=nhauntersR-2/360=LR/2

Tangentlinelength=d-(R-R)externaltangentiallength

=d-(R+R)

Thetwocirclesareintersectingd=R+R(R+R).Thetwo

circlesareintersectingR-R(R+R),andthetwocirclesare

intersectingd=R-R(R>R).

Thetwocirclesoftheintersectinglineperpendiculartothe

commonstringofthetwocircles

Theoremofthecircleisdividedinton(n3orhigher):(1)

linkeachpointoftheproceedsofthepolygonisthiscircle

isinscribedinanside2aftereachcircletangenttothe

equinox,adjacenttothetangentintersectionofverticesof

polygonistheroundcircumscribedisnside

Theoremanypositivepolygonhasanoutercircleandaninner

circle,andthesetwocirclesareconcentriccircles

IfyouhaveanykaroundavertexisnedgeAngle,becauseof

theAngleandshouldbe360°,sok*(n-2)°to1800/

n=360(n-2)-2(k)=4

Arclengthcalculationformula:L=n-R/180

Fanareaformula:Sfan=nhauntersR'2/360=LR/innercommon

tangentlength=d-2146(R-R)toconstructthelong=d-

(R+R)

Mathematicalformulaforjuniorhighschool:thesourceofthe

formulaforfactoringintheformula:theauthorofthearticle:

purplehan,2013-03-1314:29:05

Formula:"33+b+c~3-3ABC=(a+b+c)(a"2+b"

2+c'2-ab-BC-ca)

Equationofsquarevariance:asquaredminusbsquared=(a+

b)(a-b)

Thetotalsumofsquaresandformulas:(a+b)squared=a

squared+2ab+bsquared

Equationoftotalsquarevariance:(a-b)squared=asquared

-2ab+bsquared

Tworadical:ax"2+c=a+bx[x-(b+)(b2-4ac))/2

a)][x-(a-b-)(b2-4ac))/2a]tworadicalexpression

Cubicandformula:a*3+b"3=(a+b)(a'2-ab+b"

2)

Statevarianceformula:a"3"3-b=(a-b)(a'2+ab+

b-2)

Completecubicformula:a"3+3a*2+3bab2+b3

=(a+b)3.

Mathematicalformulaofjuniorhighschool:quadraticequation

formulaanddiscriminantsource:purplehan2013-03-13

14:33:21

Thesolutionofthequadraticequationisminusbplusthe

squarerootofb2minus4acover2aminusthesquarerootof

b2minus4acover2a

TherelationbetweentherootandthecoefficientisXIplus

X2isequaltominusb/aXItimesX2isequaltoc/a

discriminant

B2-4ac=0note:theequationhastwoequalrealroots

B2-4ac>note:theequationhastwodifferentrealroots

B2-4ac<0note:theequationhasnorealrootsandhasconjugate

complexroots

Middleschoolmathematicsformula:trigonometricinequality

source:theauthorofthepaper:purplehan2013-03-1314:31:38

a|orlessa+b+b

a-b+baorless

a|b<=>-orlessba,borlessorless

a-bp||-|b|-|a|bla|orlessorless

Mathematicalformulaofjuniorhighschool:arithmeticof

arithmeticprogressionformula:Chinesepaper:purplehan

2013-03-1314:50:37

Someofthetopnentries

1+2+3+4+5+6+7+8+9+…+n=n(n+1)/21+

3+5+7+9+11+13+15+...+(2n-1)=n2

2+4+6+8+10+12+14+...+(2n)=n(n+1)32+42

+12+22++62+72+82+52...+n2=n(n+1)(2n+1)

/6

13+23++43+53+63+...N32/41=n2(n+1)*2+2+

3*3*4+4*6+5+5**7+…+n(n+1)=n(n+1)

(n+2)/3

Twoanglesandformulas

Sin(A+B)=sinAcosB+cosAsinB

Sin=sinAcosB-sinBcosA(A-B)

Cos(A+B)=cosAcosB-sinAsinB

Cos(A-B)=cosAcosB+sinAsinB

Tan(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

Formulaofmathematicaltrigonometricfunctionofjuniorhigh

school:doubleAngleformula.Author:purplehan2013-03-13

14:44:18

DoubleAngleformula

Tanatan2A=2/(1-tan2A)

Ctg2A=ctga(ctg2A-1)/2

Cos2a=cos2a-cos2asin2a=2-1=1-2sin2a

Middleschoolmathematicstrigonometricfunctionformula:a

halfAngleformulasource:middleexaminationnetworkarticle

author:purplehan2013-03-1314:46:27

HalfAngleformula

(sin(A/2)=)(1-cosA)/2)sin(A/2)=-)((1-cosA)

/2)

(cos(A/2)=)(1+cosA)/2)cos(A/2)=-)((1+cosA)

/2)

Tan(A/2)=)((1-cosA)/((1+cosA))tan(A/2)=(1-cosA)

(-)/((1+cosA))

CTG(A/2)=)((1+cosA)/((1-cosA))withinitiative(A/

2)=(1+cosA)(-)/((1-cosA))

Formulaofmathematicaltrigonometricfunctionofjuniorhigh

school:anddifferentialproductsource:theauthorofChinese

testnet:purplehan2013-03-1314:49:03

Anddifferentialproduct

2sinacosb=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(cosa(A-B)/2+cosB

=2cos((A+B)/2)sin(A-B)/(2)

TanA+tanB=sin(A+B)/cosAcosBtanA-tanB=sin(A-

B)/cosAcosB

CtgA+ctgBsin(A+B)/sinAsinBctgA+ctgBsin(A+B)/sinAsinB

Themathematicaltheoremofmiddleschool:theoriginofthe

theoryofproportionproperties:theauthorofthearticle:

purplehan,2013-03-1410:34:40

(1)thebasicnatureoftheratio

Ifa:b=c:d,thenAD=BCifAD=BC,thena:b=c:d

(2)theratioproperty

Ifa/bisequaltoc/d,then(aplusorminusb)/b=(c+/-

d)/d

(3)geometricproperties

Ifa/b=c/d=...It'smovern(b+d+...+nnot0),so(a

+c+...+m)/(b+d+...+n)=a/b

Thetheoremofthemathematicscircleofjuniorhighschool:

theauthorofthearticle:purplehan2013-03-1218:05:52

Thethreepointsofthenoncollineardetermineacircle

Itcanbedoneinanumberofcircles

Aftertwopoints,youcanalsomakecountlesscircles,andthe

centerofthecircleisintheverticalbisectoroftheline

betweenthetwopoints

Theorem:threepointsthatarenotcollinear,canbedoneand

onlyonecirclecanbemade

Corollary:thetriangle'sthree-sideverticalbisecting1ine

intersectsatonepoint,whichistheoutsideofthetriangle

Theintersectionofthreehighlinesofatriangleiscalled

atriangle

1.3verticalpaththeorem

Thecircleisthecentralsymmetricfigure;Thecenterofthe

centeristhecenterofsymmetry

Thecircleisasymmetricalgraphoftheweek,andanyline

throughthecenterofthecircleisitsaxisofsymmetry

Theorem:perpendiculartothediameterofthestringbisects

thisstring,andthescorestringhastwoarcstoit

Corollary1:dividethediameterofthestring(notthediameter)

perpendiculartothestringandbisectthetwoarcsofthe

string

Corollary2:theverticalhalfofthestringisdividedbythe

centerofthecircle,andthetwoarcsofthestringarebisected

Corollary3:thediameterofanarcthatthestringisopposite,

theverticalscorestring,andtheotherarcthatthestring

isright

1.4arc,chordchorddistance

Theorem:inthesamecircleorequalcircle,theequalarcis

equaltothestring,thechordofthestringisequaltothe

centerofthestring

Therelationshipbetweenthetwocirclesandtheline

2.1therelationshipbetweenthecircleandtheline

Ifalineandacirclehavenocommonpoint,thenwesaythat

thislineisgoingtogoawayfromthiscircle

Ifalineandacirclehaveonlyonecommonpoint,let'ssay

thatthislineistangenttothiscircle,andthislineiscalled

thetangentofthecircle,andthispublicpointiscalledthe

tangentofthem

Theorem:theoutsideoftheradiusofthecircle,andtheline

perpendiculartotheradiusisthetangentofthecircle

Theorem:thetangentofacircleisperpendiculartotheradius

ofthetangent

Corollary1:astraightlinethatiscenteredandperpendicular

tothetangentlinemustbetangent

Corollary2:thelinethatpassesthroughthetangentandis

perpendiculartothetangent1inewillpassthroughthecenter

ofthecircle

Ifalineandacirclehavetwopublicpoints,let'ssaythat

thislineintersectsthecircle,andthislineiscalledthe

secantofthecircle,andthesetwopublicpointsarecalled

theintersections

Therelationshipbetweenastraightlineandacirclecanonly

berelatedtothephase,tangentandintersecting

2.2theinnercircleofthetriangle

Ifthesidesofapolygonlieinastraightline,itistangent

toacircle,whichiscalledtheoutercutpolygonofthecircle,

andthiscircleiscalledtheinnercircleofthepolygon

Theorem:thethreeanglesofatrianglearebisectedinone

point,whichistheinnerpartofthetriangle

Theangularscoringlineofatriangleandtheouteranglesof

theothertwoanglesaregiventoapoint,whichiscalledthe

paragonofthetriangle.Thecenterofthecentercanbeacircle

andonesideandtheothersideoftheextensioncord,andthe

circleiscalledthesidecuttingcircleofthetriangle

2.3tangentlengththeorem

Theorem:twotangentsofthecirclefromtheoutsideofthe

circle,thetangentoftheirfaces,thecenterofthecircle

andthelineofthispointaredividedbetweenthetwotangents

Theoutsideofthe2.4circle

Theorem:thetwopairsofsidesoftheoutertangentofacircle

areoppositeandequal

Theorem:ifthequadranglepairsareequaltoeachother,then

ithastohaveaninnercircle

Therelationshipbetweenthethreecirclesandthecircle

3.1positionrelationshipoftwocircles

Intheplane,twocirclesthatdon'toverlap.Theirposition

relationhasthefollowingfiveconditions:external,external,

intersecting,intersecting,andtangential

Aftertwocirclesofthecenterofacircle,itiscalleda

two-roundline,andthedistancebetweenthetwocirclesis

calledthecenterdistance

Theorem:thetwocirclesofthecenterlinearetheaxisof

symmetryofthetwocircles,andwhenthetwocirclesare

tangenttoeachother,theyaretangenttotheconcentricline

(1)twocirclesoutofd>R+R

(2)twocircles

(3)thetwocirclesintersectR-R<R+R(R>R)

(4)tangentd=r-r(R,BBB0R)

(5)twocirclescontaind<R-R(RBBB0R).

Inparticular,thetwocirclesareconcentriccirclesd=0

3.2thecommontangentoftwocircles

Theorem:theappearanceoftwooutertangentlinesoftwo

circles;Thelengthofthetangentlineoftwocirclesisequal

Mathematicalformulatheoremofjuniorhighschool:

trigonometricfunctiontheoremsource:middleschoolpaper

author:purplehan2013-03-1313:54:06

ThesineofanyacuteAngleisequaltothecosineofits

remainingAngle,andthecosineofanyacuteAngleisequalto

thesineofitsremainingAngle

ThetangentvalueofanyacuteAngleisequaltotheresidual

tangentofitsremainingAngle,andtheresidualvalueofany

acuteAngleisequaltothetangentofitsremainingAngle

Mathematicalformulatheoremofjuniorhighschool:asimilar

triangletheoremsource:Chinesepaperauthor:purplehan

2013-03-1313:47:51

Similartriangletheorem:thelinethatisparalleltooneside

ofthetriangleintersectsbothsides(orextensioncordson

bothsides),andthetriangleformedissimilartotheoriginal

triangle

Similartriangledecisiontheorem1:thetwoanglescorrespond

toeachother,andthetwotrianglesaresimilar(ASA)

Thetworighttrianglesofarighttrianglearesimilartothe

originaltriangles

Theorem2:thetwosidesareproportionalandtheAngleisequal,

thetwotrianglesaresimilar(SAS)

Decisiontheorem3:threesidescorrespondingtoproportional,

twotriangularsimilarity(SSS)

Similarrighttriangletheorem:ifthehypotenuseofaright

triangleandasquareedgeandtheotherofthehypotenuseof

arighttriangleandacorrespondingisproportionaltothe

squareedge,thenthetwosimilarrighttriangle

Propertytheorem1:similartrianglescorrespondtohigher

ratiosthanthecorrespondinganglesofthecorresponding

angularbisectors

Theorem2:theratioofasimilartriangleissimilartothat

ofasimilartriangle

Theorem3:theratioofsimilartriangularareasisequalto

thesquareofthesimilarratio

Mathematicalformulatheoremofjuniorhighschool:middle

positionlinetheoremsource:purplehan2013-03-1313:42:20

Themedianlinetheoreminthetriangle:themedianlineofa

triangleisparalleltothethirdside,andisequaltohalf

ofit

Themedianlinetheoremintrapezoid:themedianlineofthe

trapezoidisparalleltothebaseoftwo,andisequaltohalf

ofthebaseandthehalfofL=(a+b),whichmeansthat2S

=L*h

Thetheoremofmathematicalformulaofjuniorhighschool:the

theoremofrectangle:theauthorofthearticle:purplehan

2013-03-1313:29:07

Rectangularpropertytheorem1:thefourcornersofthe

rectanglearerightangles

Theorem2:rectangulardiagonalsareequal

Rectangledeterminationtheorem1:therearethreecornersthat

arerectangularandrectangular

Rectangledeterminationtheorem2:theparallelogramofthe

diagonalisarectangle

Mathematicsformulatheoremofjuniorhighschool:rhombic

theoremsource:zeng.comarticleauthor:purplehan2013-03-13

13:31:10

Diamondpropertytheorem1:thefoursidesofthediamondshape

areequal

Diamondpropertytheorem2:rhombicdiagonallinesare

perpendiculartoeachother,andeachdiagonalisbisectedin

pairs

Thediamondareaisequaltohalfofthediagonalproduct,which

isS=(acrossb)2

Diamonddeterminationtheorem1:quadrilateralwithequal

sidesisdiamondshape

Diamonddeterminationtheorem2:aparallelogramperpendicular

tothediagonalisadiamond

Mathematicsformulatheoremofjuniorhighschool:thesquare

theoremsource:theauthoroftheart