初中数学内容（Junior high school mathematics content）

初中数学内容(Juniorhighschoolmathematicscontent)

Mathematicalknowledgeinductioninjuniorhighschool

Additionoperationofrationalnumbers

ThesamenumberLiangshulaisumofabsolutevaluewithconstant

number.

Numbersadded,large,reduced,bignumbers,decisionsand

symbols.

Theoppositeisthesumofnumbers,andtheresultiszero.

[note]"big"minus"small"referstotheabsolutesize.

Subtractionofrationalnumbers

Minusequalsplusminus,plusminusequalsplus.

Multiplicationofrationalnumbers;symboliclaws

Thesamenumberispositive,theoppositenumberisnegative,

oneiszero,andtheproductiszero.

collect

Speakingofthemergerofsimilaritems,thelawmustnot

forget.

Justaskforthecoefficientsalgebraandthealphabetindex

toremainthesame.

Goandaddthebracketrule

Tobracketoraddparentheses,thekeydependsontheconnection

number.

Thefrontisexpanding,plus,toaddparenthesesconstant

number.

Infrontofthebracketsisnegativetoaddbracketsare

variable.

Solveequations

Knownunknownseparation,separationdependsonthecompletion

ofthemove.

Howtochangeandshiftandchange,inadditiontomoving

variablebyvariable.

Squaredifferenceformula

Thedifferenceisequaltothenumberandmultiplication,

squaredifference.

Itisnotthesumofthetwotermsofaccretionanddifference.

Completesquareformula

Dimeroussumordifferencesquare,atotalofthreeofits

expansion.

Firstsquareandlastsquare,firstandlasttwotimes.

Thesumofsquaresofasumisfirstreducedandthenaddedto

thesumofsquares.

Completesquareformula

Thefirstsquareandthelastsquare,twotimesattheendof

thecenter.

Thesumofsquaresplusthesumofthefirstminusthesum

squared.

Solvingaunaryequation

Gotothedenominatorinparentheses,revenuervariableto

remember.

Similartothemerger,thecoefficientof"1"isnotgood.

Seektheunknown,betested,returnthevalue,andsoon.

Solvingaunaryequation

Gotothedenominatorinparentheses,transposethemergerof

similaritems.

Coefficientof1isnotgood,accurate,notwhitebusy.

Factoringandmultiplication

Sumdifferenceproductismultiplication,multiplication

itselfisoperation.

Integrationanddifferencearefactorization,factorization,

nonoperation.

Factorization

Twosquaresymboldifferent,factoringyoudon,tfear.

Twobottomandmultiplytwobottomdifference,decomposition

resultisit.

Twosquaresymbolwiththebottomoftheproduct2timessitting

inthecenter.

Thefactorizationcanordoesnot,thesymbolhasthearticle

above.

Thesameandthedifferencefirstsquare,butalsoplusplus

sign.

Sameregular,positiveandnegativeisnegative,butdifferent

needtoaddpowersymbol.

Factorization

Mentiontwosetsofthreegroups,crossmultipliedalsoonthe

number.

Fourmethodsarenotavailable,thedemolitionitemsTimitems

torestructure.

Trysolvingreorganizationhopeless,changeelementor

remainder.

Avarietyofflexiblemethods,theseresultsarethebasisfor.

Ifthesametypemultiplication,powersaidtoremember.

[note]twosetsofformulas(setsofformulas)

Factorization

Atwosetofthreegroups,alsothenumberofrootsofproduct.

Fivemethodsarenotavailable,thedemolitionitemsTimitems

torestructure.

Anantidoteagainstthediseasesteady,theseresultsarethe

basisfor.

Factorizationofthetwothreeterms

Thinkofthecompletesquareformula,andthecross

multiplicationisnext.

Twokindsofmethoddoesn，twork,trytorootdecomposition.

Ratioandproportion

Thedivisionisalsocalledthetworatioisequaltothe

proportionofcall.

Outgoingproductitemswithinaproduct,productofeightratio

etc..

Eachexchangeofinternalandexternalterms,allmustbecalled

morethan.

Atthesametimeexchangeofinternalandexternalterms,we

shouldcallitaninverseratio.

Beforeandafterthelatterandcalled,theratioconstant

ratio.

Beforeandaftercontrastratioisbetterthanthelatter.

Anequalratiooftwoentriestotwo.

Theratioandconsequentandratioofgeometricinvariant

called.

Solutionproportion

Outgoingproductitemwithintheproductlist,andsolvingthe

equation.

Seekingratio

Fromtheknowntoseektheratio,avarietyofwayscanbeused.

Usetheproportionofsevenproperties,variablereplacement

isalsopopular.

Eliminationisalsoagoodway,theywillwork.

Positiveratioandinverseproportion

Proportionaltotheagreedvariable,

Theproductisinverselyproportionaltothevariable.

Positiveratioandinverseproportion

Thequotientofthechangeprocessmustbeproportionaltothe

twovariables.

Theproductofachangemustbeinverselyproportionaltothe

twovariables.

Yourjudgmentisproportionalto

Fourthisproportionalto,increasingordecreasingsorting.

Bothendsoftheintermediateproductproduct,acertain

proportionofdigits.

Judgetheproportionofthefourformula

Thefourtypeisproportionalto,ordescendingsorting.

Attheendoftheproduct,suchasthemiddleproduct,thefour

formcanbeproportional.

Themean

Asaproportionoffour,thesamefacilitywillmeet.

Sometimesthebalancewillbethesame,notmeanproportional.

Themeanisveryimportant,willencounteravarietyof

occasions.

Asaproportionoffourinthesamefacility,therearemany.

Sometimesthebalancewillbethesame,themeanproportional.

Withthenumberofsquareofproduct,themeannoescape.

Radicalandirrational

Saidtherootofthealgebracanbecalledradical.

Isdifferentfromunreasonable,beopenwithoutlimit.

Therearelettersinthewaythatcanbecalledirrational.

Unreasonabletypeisradical,todistinguishthemwiththe

sign.

Therearelettersinthewayofopening,andtheycanbecalled

irrational.

Definedomain

Thedefinitionofthedomainisexquisite,andthefour

principlesmustbepaidattentionto.

Negativenumberscannotbesquared,denominatoriszero,

meaningless.

Thatisnotthebottomfractionofpositive,zerozeropower.

Therestrictionsarenotuniquetosatisfymultiple

inequalities.

Definethedomaintopass,andthefourprinciplesmustpay

attention.

Negativenumberscannotbesquared,denominatoriszero,

meaningless.

Thebottomfractionofpositive,zeronopowerofzero.

Restrictedcondition,nonuniqueness,solutionsetof

inequalitygroup.

Solvingaunaryinequality

Gotothedenominatorinparentheses,transposethemergerof

similaritems.

Thecoefficientof"1"attention,withnegativechangetobe.

Gotothedenominatorinparentheses,don'tforgettochange,

revenuer.

Thesamekindofmerger,coefficientof"1"attention.

Thesameistobewithouthindrance,withnegativechange,

multiplicationanddivision.

Solutionofoneyuaninequalities

Largerthanthehead,smallerthanthetail,thesizeofthe

middle,lookingfor.

Bigandsmallwithoutsolution,thefourkindofsituationall

came.

Takethesamedirection,taketheoppositedirectionandtake

themiddle.

Thereisnoelementinthemiddle,nosolutionappears.

Childreninkindergartenaresmall

Oldpeople'shomesareproudofoldage

Therewerenooldsoldiersinthecamp,(small,big,that,sit)

Largesizesolutioninspace,(small,big,wow!)

Solutionofatwodegreeinequality

Firstintogeneral,constructorsecondstops.

Ifthediscriminantvalueisnotnegative,thecrosssection

ofthecurvehasanintersectionpoint.

Aisopening.It'supandoverzero.Takebothsides.

Ifthealgebraicformulaislessthanzero,thesolutionsets

areintersectionnumbers.

Ifthesquarehasnorealroot,thebigzerosolutiononthe

mouthisall.

Lessthanzerowillhavenosolution.Theopeningisthe

opposite.

Factoringbythesquaredifferenceformula

Differentnumberstwosquareterms,factoring,thereareways.

Twobottomandmultiplytwobottomdifference,decomposition

resultisit.

Factorizationbymeansofthesquareformula

Twosquareitemsatbothends,bottom2timesinthemiddle.

Thesameistruebetweenthetwobaseandthesquare,thetotal

negativeandtheoppositenumber.

Dividedintotwobasedifferencesquare,founderdoubleproduct

tonegative.

Thetwosidesarenegative,themiddleisright,andthebase

differenceistheopposite.

Onesquareanothersquare,thebottomproduct2timesinthe

middle.

Attheendoftwoandthreesquare,fullofnegativeandopposite

party.

Dividedintotwobasedifferencesquares,bothendsare

positivetimes,productnegative.

Ifbothsidesarenegative,themiddleisrightandthebase

differenceistheopposite.

Solutionoftwoequationofoneelementbyformula

Tosolvetheequationbyformula,itisfirstgeneralized.

Thecoefficientofadjustmentfollows,makingitthesimplest

ratio.

DeterminetheparameterABC,andcalculatetheequation

discriminant.

Thediscriminantvalueandthezeroratioareknown.

Arealrootcanbesetformula,thereisnorealroottobe

reported.

Solvingtheequationoftwovariablesofoneelementwiththe

conventionalmethod

Left,left,rightfirstseparated,

Two,"1"isnext.

Abinarysquare,onbothsideswithnoproblem.

Therighttoopendirectdecompositionmerger,problemsolving.

Thissolutioniscalledformula,anditismorepracticewhen

solvingequation.

Solutionoftwoequationofoneelementbyindirect

distributionmethod

Theknownunknownsarefirstseparated,andthefactorization

isfollowed.

Adjustmentcoefficients,suchasreciprocalanddifference

sets,identities.

Completesquareequalconstant,indirectformula,obvious

advantage

[notes]identities

Solvingthetwoequationofonevariable

Nooneitem,themostidealdirectextraction.

Ifaconstanttermismissing,factoringisnotdiscussed.

B,Careequaltozero,andsorootiszero,don'tforget.

BandCarenotzero,factoringorformulaatthesametime,

Canalsobedirectlysetformula,dependingontheproblem

varieschoicerecipe.

Identificationofpositiveproportionfunction

Checkthepositiveproportionfunction,andtestitintwo

steps.

Aquantityrepresentsanotherquantity,

Juniorhighschoolmathematicsformula

ShanghaiTongZhoumodelschoolSongLifeng

Additionoperationofrationalnumbers

ThesamenumberLiangshulaisumofabsolutevaluewithconstant

number.

Numbersadded,large,reduced,bignumbers,decisionsand

symbols.

Theoppositeisthesumofnumbers,andtheresultiszero.

[note]"big"minus"small"referstotheabsolutesize.

Subtractionofrationalnumbers

Minusequalsplusminus,plusminusequalsplus.

Multiplicationofrationalnumbers;symboliclaws

Thesamenumberispositive,theoppositenumberisnegative,

oneiszero,andtheproductiszero.

collect

Speakingofthemergerofsimilaritems,thelawmustnot

forget.

Justaskforthecoefficientsalgebraandthealphabetindex

toremainthesame.

Goandaddthebracketrule

Tobracketoraddparentheses,thekeydependsontheconnection

number.

Thefrontisexpanding,plus,toaddparenthesesconstant

number.

Infrontofthebracketsisnegativetoaddbracketsare

variable.

Solveequations

Knownunknownseparation,separationdependsonthecompletion

ofthemove.

Howtochangeandshiftandchange,inadditiontomoving

variablebyvariable.

Squaredifferenceformula

Thedifferenceisequaltothenumberandmultiplication,

squaredifference.

Itisnotthesumofthetwotermsofaccretionanddifference.

Completesquareformula

Dimeroussumordifferencesquare,atotalofthreeofits

expansion.

Firstsquareandlastsquare,firstandlasttwotimes.

Thesumofsquaresofasumisfirstreducedandthenaddedto

thesumofsquares.

Completesquareformula

Thefirstsquareandthelastsquare,twotimesattheendof

thecenter.

Thesumofsquaresplusthesumofthefirstminusthesum

squared.

Solvingaunaryequation

Gotothedenominatorinparentheses,revenuervariableto

remember.

Similartothemerger,thecoefficientof"1"isnotgood.

Seektheunknown,betested,returnthevalue,andsoon.

Solvingaunaryequation

Gotothedenominatorinparentheses,transposethemergerof

similaritems.

Coefficientof1isnotgood,accurate,notwhitebusy.

Factoringandmultiplication

Sumdifferenceproductismultiplication,multiplication

itselfisoperation.

Integrationanddifferencearefactorization,factorization,

nonoperation.

Factorization

Twosquaresymboldifferent,factoringyoudon,tfear.

Twobottomandmultiplytwobottomdifference,decomposition

resultisit.

Twosquaresymbolwiththebottomoftheproduct2timessitting

inthecenter.

Thefactorizationcanordoesnot,thesymbolhasthearticle

above.

Thesameandthedifferencefirstsquare,butalsoplusplus

sign.

Sameregular,positiveandnegativeisnegative,butdifferent

needtoaddpowersymbol.

Factorization

Mentiontwosetsofthreegroups,crossmultipliedalsoonthe

number.

Fourmethodsarenotavailable,thedemolitionitemsTimitems

torestructure.

Trysolvingreorganizationhopeless,changeelementor

remainder.

Avarietyofflexiblemethods,theseresultsarethebasisfor.

Ifthesametypemultiplication,powersaidtoremember.

[note]twosetsofformulas(setsofformulas)

Factorization

Atwosetofthreegroups,alsothenumberofrootsofproduct.

Fivemethodsarenotavailable,thedemolitionitemsTimitems

torestructure.

Anantidoteagainstthediseasesteady,theseresultsarethe

basisfor.

Factorizationofthetwothreeterms

Thinkofthecompletesquareformula,andthecross

multiplicationisnext.

Twokindsofmethoddoesn'twork,trytorootdecomposition.

Ratioandproportion

Thedivisionisalsocalledthetworatioisequaltothe

proportionofcall.

Outgoingproductitemswithinaproduct,productofeightratio

etc..

Eachexchangeofinternalandexternalterms,allmustbecalled

morethan.

Atthesametimeexchangeofinternalandexternalterms,we

shouldcallitaninverseratio.

Beforeandafterthelatterandcalled,theratioconstant

ratio.

Beforeandaftercontrastratioisbetterthanthelatter.

Anequalratiooftwoentriestotwo.

Theratioandconsequentandratioofgeometricinvariant

called.

Solutionproportion

Outgoingproductitemwithintheproductlist,andsolvingthe

equation.

Seekingratio

Fromtheknowntoseektheratio,avarietyofwayscanbeused.

Usetheproportionofsevenproperties,variablereplacement

isalsopopular.

Eliminationisalsoagoodway,theywillwork.

Positiveratioandinverseproportion

Theagreedvariableswereproportionaltotheproductvariables

andinverselyproportionaltothesetvariables.

Positiveratioandinverseproportion

Thequotientofthechangeprocessmustbeproportionaltothe

twovariables.

Theproductofachangemustbeinverselyproportionaltothe

twovariables.

Yourjudgmentisproportionalto

Fourthisproportionalto,increasingordecreasingsorting.

Bothendsoftheintermediateproductproduct,acertain

proportionofdigits.

Judgetheproportionofthefourformula

Thefourtypeisproportionalto,ordescendingsorting.

Attheendoftheproduct,suchasthemiddleproduct,thefour

formcanbeproportional.

Themean

Asaproportionoffour,thesamefacilitywillmeet.

Sometimesthebalancewillbethesame,notmeanproportional.

Themeanisveryimportant,willencounteravarietyof

occasions.

Asaproportionoffourinthesamefacility,therearemany.

Sometimesthebalancewillbethesame,themeanproportional.

Withthenumberofsquareofproduct,themeannoescape.

Radicalandirrational

Saidtherootofthealgebracanbecalledradical.

Isdifferentfromunreasonable,beopenwithoutlimit.

Therearelettersinthewaythatcanbecalledirrational.

Unreasonabletypeisradical,todistinguishthemwiththe

sign.

Therearelettersinthewayofopening,andtheycanbecalled

irrational.

Definedomain

Thedefinitionofthedomainisexquisite,andthefour

principlesmustbepaidattentionto.

Negativenumberscannotbesquared,denominatoriszero,

meaningless.

Thatisnotthebottomfractionofpositive,zerozeropower.

Therestrictionsarenotuniquetosatisfymultiple

inequalities.

Definethedomaintopass,andthefourprinciplesmustpay

attention.

Negativenumberscannotbesquared,denominatoriszero,

meaningless.

Thebottomfractionofpositive,zeronopowerofzero.

Restrictedcondition,nonuniqueness,solutionsetof

inequalitygroup.

Solvingaunaryinequality

Gotothedenominatorinparentheses,transposethemergerof

similaritems.

Thecoefficientof"1"attention,withnegativechangetobe.

Gotothedenominatorinparentheses,don'tforgettochange,

revenuer.

Thesamekindofmerger,coefficientof"1"attention.

Thesameistobewithouthindrance,withnegativechange,

multiplicationanddivision.

Solutionofoneyuaninequalities

Largerthanthehead,smallerthanthetail,thesizeofthe

middle,lookingfor.

Bigandsmallwithoutsolution,thefourkindofsituationall

came.

Takethesamedirection,taketheoppositedirectionandtake

themiddle.

Thereisnoelementinthemiddle,nosolutionappears.

Childreninkindergartenaresmall

Oldpeople,shomesareproudofoldage

Therewerenooldsoldiersinthecamp,(small,big,that,sit)

Largesizesolutioninspace,(small,big,wow!)

Solutionofatwodegreeinequality

Firstintogeneral,constructorsecondstops.

Ifthediscriminantvalueisnotnegative,thecrosssection

ofthecurvehasanintersectionpoint.

Aisopening.It'supandoverzero.Takebothsides.

Ifthealgebraicformulaislessthanzero,thesolutionsets

areintersectionnumbers.

Ifthesquarehasnorealroot,thebigzerosolutiononthe

mouthisall.

Lessthanzerowillhavenosolution.Theopeningisthe

opposite.

Factoringbythesquaredifferenceformula

Differentnumberstwosquareterms,factoring,thereareways.

Twobottomandmultiplytwobottomdifference,decomposition

resultisit.

Factorizationbymeansofthesquareformula

Twosquareitemsatbothends,bottom2timesinthemiddle.

Thesameistruebetweenthetwobaseandthesquare,thetotal

negativeandtheoppositenumber.

Dividedintotwobasedifferencesquare,founderdoubleproduct

tonegative.

Thetwosidesarenegative,themiddleisright,andthebase

differenceistheopposite.

Onesquareanothersquare,thebottomproduct2timesinthe

middle.

Attheendoftwoandthreesquare,fullofnegativeandopposite

party.

Dividedintotwobasedifferencesquares,bothendsare

positivetimes,productnegative.

Ifbothsidesarenegative,themiddleisrightandthebase

differenceistheopposite.

Solutionoftwoequationofoneelementbyformula

Tosolvetheequationbyformula,itisfirstgeneralized.

Thecoefficientofadjustmentfollows,makingitthesimplest

ratio.

DeterminetheparameterABC,andcalculatetheequation

discriminant.

Thediscriminantvalueandthezeroratioareknown.

Arealrootcanbesetformula,thereisnorealroottobe

reported.

Solvingtheequationoftwovariablesofoneelementwiththe

conventionalmethod

Theleft,theleftandtherighthaveseparatedfirst,andthe

twoseriesof"1"issecond.

Abinarysquare,onbothsideswithnoproblem.

Therighttoopendirectdecompositionmerger,problemsolving.

Thissolutioniscalledformula,anditismorepracticewhen

solvingequation.

Solutionoftwoequationofoneelementbyindirect

distributionmethod

Theknownunknownsarefirstseparated,andthefactorization

isfollowed.

Adjustmentcoefficients,suchasreciprocalanddifference

sets,identities.

Completesquareequalconstant,indirectformula,obvious

advantage

[notes]identities

Solvingthetwoequationofonevariable

Nooneitem,themostidealdirectextraction.

Ifaconstanttermismissing,factoringisnotdiscussed.

B,Careequaltozero,andsorootiszero,don，tforget.

BandCarenotzero,factoringorformulaatthesametime,

Canalsobedirectlysetformula,dependingontheproblem

varieschoicerecipe.

Identificationofpositiveproportionfunction

Checkthepositiveproportionfunction,andtestitintwo

steps.

Aquantityindicatingwhetheranotherquantityistrueornot.

Ifyouhavetolookatthevalue,alltherealnumbersshould

bethere.

Whetherapositivescalefunctionisdistinguishedshouldbe

dividedintotwosteps.

Aquantityindicatesanotherquantity,isthere?.

Ifwelookatthevalueagain,allrealnumbersareneeded.

Therearetwostepstomeasuringapositivescalefunction.

Aquantityindicatingwhetheranotherquantityistrueornot.

Ifyouhavetolookatthevalue,alltherealnumbersshould

bethere.

Theimageandpropertyofpositiveproportionfunction

Proportionalfunctiondiagram,straightline,passingand

origin.

Kisthreeminus24,thechangetendencyisrecordedbetween

theheart.

Kislowontheleft,highontheright,andclimbingwith

datong.

Knegativehighleftlowontheright,theotherasmallmountain

crest.

Primaryfunction

Afunctiondiagram,straightline,passingpoint.

Kislowtotheleft,hightotheright,andgoeshigherand

highertoclimbthemountain.

Knegative,lefthigh,lowright,lowerandlower,isobvious.

KsaystheslopeisB,theinterceptiszero,andthechange

ispositive.

Inversescalingfunction

Inversefunction,hyperbola,passingpoint.

Kisthreeminus24,twoisitsasymptote.

Kislefthigh,therightislow,andthe13quadrantslides

downthemountain.

Knegativeleft,righthigh,24quadrant,suchasclimbing.

Twofunction

Thetwoequation,thezerochangey,thetwofunctionappears.

Allrealnumbersdefinethedomain,andtheimageiscalled

parabola.

Aparabolahasasymmetrical