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初中數(shù)學(xué)內(nèi)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
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