人教版初一數(shù)學(xué)知識點匯總(打印版)-2023修改整理

千里之行，始于足下讓知識帶有溫度。第第2頁/共2頁精品文檔推薦人教版初一數(shù)學(xué)知識點匯總(打印版)

七年級數(shù)學(xué)（上）學(xué)問點

人教版七年級數(shù)學(xué)上冊主要包含了有理數(shù)、整式的加減、一元一次方程、圖形的熟悉初步四個章節(jié)的內(nèi)容.

第一章有理數(shù)

一．學(xué)問框架

二．學(xué)問概念

1.有理數(shù)：

(1)凡能寫成)0

p

q,p(

p

q

≠

為整數(shù)且形式的數(shù)，都是有理數(shù).正整數(shù)、0、負整數(shù)統(tǒng)稱整數(shù)；正分數(shù)、負分數(shù)統(tǒng)稱分數(shù)；整數(shù)和分數(shù)統(tǒng)稱有理數(shù).注重：0即不是正數(shù)，也不是負數(shù)；-a不一定是負數(shù)，+a也不一定是正數(shù)；π不是有理數(shù)；

(2)有理數(shù)的分類:①

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負分數(shù)

負整數(shù)

負有理數(shù)

零

正分數(shù)

正整數(shù)

正有理數(shù)

有理數(shù)②

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負分數(shù)

正分數(shù)

分數(shù)

負整數(shù)

零

正整數(shù)

整數(shù)

有理數(shù)

2．?dāng)?shù)軸：數(shù)軸是規(guī)定了原點、正方向、單位長度的一條直線.

3．相反數(shù)：

(1)惟獨符號不同的兩個數(shù)，我們說其中一個是另一個的相反數(shù)；0的相反數(shù)還是0；

(2)相反數(shù)的和為0?a+b=0?a、b互為相反數(shù).

4.肯定值：

(1)正數(shù)的肯定值是其本身，0的肯定值是0，負數(shù)的肯定值是它的相反數(shù)；注重：肯定值的意義是數(shù)軸上表示某數(shù)的點離開原點的距離；

(2)肯定值可表示為：

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=

)0

a(

a

)0

a(

)0

a(

a

a或

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0,decimal-largenumber<0.

6.Reciprocalofeachother:Twonumberswhoseproductis1arereciprocalofeachother;Note:0hasnoreciprocal;ifa≠0,thenthereciprocalis;ifab=1a,barereciprocalofeachother;ifab=-1aAndbarenegativereciprocals.

7.Thelawofadditionofrationalnumbers:

(1)Addtwonumberswiththesamesign,takethesamesign,andaddtheabsolutevalue;

(2)Addtwonumberswithdifferentsigns,takethesignwithlargerabsolutevalue,andsubtractthesmallerabsolutevaluewiththelargerabsolutevalue;

(3)Ifanumberisaddedto0,youstillhavethisnumber.

8.Thearithmeticofrationalnumberaddition:

(1)Theexchangelawofaddition:a+b=b+a;(2)Thecombinationlawofaddition:(a+b)+c=a+(b+c).

9.Thelawofrationalnumbersubtraction:subtractinganumberisequaltoaddingtheoppositeofthisnumber;thatis,a-b=a+(-b).

10Therationalnumbermultiplicationrule:

(1)Thetwonumbersaremultiplied,thesamesignispositive,thedifferentsignisnegative,andtheabsolutevalueismultiplied;

(2)Anynumbermultipliedbyzerowillgetzero;

(3)Whenseveralnumbersaremultiplied,onefactoriszeroandtheproductiszero;eachfactorisnotzero,andthesignoftheproductisdeterminedbythenumberofnegativefactors.

11Operationlawofrationalnumbermultiplication:

(1)Theexchangelawofmultiplication:ab=ba;(2)Thecombinationlawofmultiplication:(ab)

c=a(bc);

(3)Thedistributionlawofmultiplication:a(b+c)=ab+ac.

12.Ruleofrationalnumberdivision:dividingbyanumberequalstomultiplyingbythereciprocalofthisnumber;note:zerocannotbedivided.

13.Thelawofpowerofrationalnumbers:

(1)Anypowerofapositivenumberisapositivenumber;

(2)Theoddpowerofnegativenumbersisnegative;theevenpowerofnegativenumbersispositive;Note:Whennisapositiveoddnumber:(-a)n=-anor(a-b)n=-(ba)n,Whennispositiveoreven:(-a)n=anor(ab)n=(ba)n.

14.Definitionofpower:

(1)Theoperationoffindingthesamefactorproductiscalledpower;

(2)Inpower,thesamefactoriscalledthebase,thenumberofthesamefactoriscalledtheexponent,andtheresultofthepoweriscalledthepower;

15.Scientificnotation:recordanumbergreaterthan10intheformofa×10n,whereaisanumberwithonlyonedigitintheintegernumber,thisnotationiscalledscientificnotation.

16.Theexactdigitoftheapproximatenumber:anapproximatenumber,roundedtothatdigit,itissaidthattheapproximatenumberisaccuratetothatdigit.

17.Significantdigits:Fromthefirstnon-zerodigitonthelefttotheexactdigits,alldigitsarecalledsignificantdigitsofthisapproximatenumber.

18.Mixedalgorithm:powerfirst,thenmultiplicationanddivision,andfinallyadditionandsubtraction.

Thecontentofthischapterrequiresstudentstocorrectlyunderstandtheconceptofrationalnumbers,basedonactuallifeandlearningthenumberaxis,tounderstandthemeaningofpositiveandnegativenumbers,oppositenumbers,andabsolutevalues.Emphasisisplacedonsolvingpracticalproblemsusingrationalnumberarithmetic.

Animportantreasonforexperiencingthedevelopmentofmathematicsisthepracticalneedsoflife.Stimulatestudents'interestinlearningmathematics,teacherstrainstudents'abilitytoobserve,generalizeandgeneralize,sothatstudentscanbuildcorrectsenseofnumbersandsolvepracticalproblems.Whenteachingthecontentofthischapter,teachersshouldcreatemoresituationstofullyreflectthesubjectivestatusofstudents'learning.

Chapter2Integeradditionandsubtraction

One.KnowledgeFramework2.KnowledgeConcept

1.Singleterm:Inanalgebraicexpression,ifitcontainsonlymultiplication(includingpower)operation.Oralthoughthereisadivisionoperation,butatypeofalgebraicexpressionswithoutlettersinthedivisioniscalledasingleterm.

2.Coefficientandfrequencyofsingleterm:Thedigitalfactorofnon-zeroinsingletermiscalledthedigitalcoefficientofsingleterm,referredtoasthecoefficientofsingleterm;whenthecoefficientisnotzero,thesumofallletterindexesinsingletermiscalledthenumberofsingleterm.

3.Polynomial:Thesumofseveralsingletermsiscalledapolynomial.

4.Thenumberanddegreeofpolynomials:thenumberofpolynomialscontainedinthepolynomialisthenumberofpolynomials.Eachpolynomialiscalledapolynomialterm;inpolynomials,thedegreeofthehighestpolynomialtermisthedegreeofpolynomial.

Throughthischapter,studentsshouldachievethefollowinglearningobjectives:

1.Understandandmastertheconceptsofsingleterms,polynomials,integers,etc.,andunderstandthedifferencesandconnectionsbetweenthem.

2.Understandtheconceptofsimilaritems,masterthemethodofmergingsimilaritems,andgraspthechangingrulesofsymbolswhenremovingparentheses,andbeabletocorrectlymergeandremoveparenthesesofsimilaritems.Onthebasisofaccuratejudgmentandcorrectcombinationofsimilaritems,integraladditionandsubtractionoperationsareperformed.

3.Understandthatlettersinintegersrepresentnumbers.Theadditionandsubtractionofintegersisbasedonthecalculationofnumbers;thebasisforunderstandingthecombinationofsimilaritemsandtheremovalofparenthesesisthedistributionlaw;theunderstandingoftheoperationlawandthenatureofoperationsintheadditionandsubtractionofintegersChinaisstillestablished.

4.Abletoanalyzethequantitativerelationshipintheactualproblemandexpressitintheformofletters.

Inthestudyofthischapter,teacherscanexperiencetheprocessofconceptformationbyallowing

studentstodiscussingroupsandcooperativelearning,etc.,toinitiallycultivatestudents'thinkingskillsandapplicationawarenesssuchasobservation,analysis,abstraction,andgeneralization.

Chapter2Unarylinearequation

One.Knowledgeframework

two.Knowledgeconcept

1.Unarylinearequation:Theintegerequationcontainingonlyanunknownnumber,andthedegreeoftheunknownnumberis1,andthecoefficientoftheunknownnumbertermisnotzeroisaunarylinearequation.

2.Thestandardformofalinearequationinonevariable:ax+b=0(xisanunknownnumber,aandbareknownnumbers,anda≠0).

3.Thegeneralstepsofthesolutiontotheunarylinearequation:sortingtheequationtothedenominatortotheparenthesesshifttermmergesimilartermscoefficientinto1(testthesolutionoftheequation).

4.Listone-dimensionallinearequationstosolvewordproblems:

(1)Theanalysismethodofreadingquestions:Itismostlyusedfor"sum,difference,times,points"

Readthequestioncarefullytofindkeywordsthatrepresentanequalrelationship,suchas:"big,small,more,less,yes,common,combined,for,complete,increase,decrease,matching",usethesekeywordsListthetextequations,andsettheunknownnumberaccordingtotheintentionofthequestion.Finally,usetherelationshipbetweenthequantityandthequantityinthetitletofillinthealgebraicformulatogettheequation.

(2)Drawinganalysismethod:…………mostlyusedfor“travelproblem”

Theuseofgraphicstoanalyzemathematicalproblemsistheembodimentofthecombinationofnumbersandshapesinmathematics.Readthequestionscarefullyanddrawtherelevantgraphicsaccordingtothemeaningoftheproblemtomakeeachpartofthegraphicshaveaspecificmeaning.Findingtheequalrelationshipthroughthegraphicsisthekeytosolvingtheproblem.Thebasisforarrangingtheequations,andfinallytherelationshipbetweenthequantityandthequantity(theunknowncanberegardedasaknownquantity),andfillingintherelevantalgebraicformulaisthebasisforobtainingtheequation.

11.Thecommonlyusedformulasofthecolumnequationstosolvetheapplicationproblems:

(1)Travelproblem:distance=speed·time;

(2)Engineeringissues:workload=ergonomicsandworkinghours;

(3)Theratioproblem:part=whole·ratio;

(4)Theproblemofforwardandreverseflow:forwardflowspeed=stillwaterspeed+waterflowspeed,reverseflowspeed=stillwaterspeed-waterflowspeed;

(5)Commoditypriceissues:sellingprice=pricing·discount·,profit=sellingprice-cost,;

(6)Perimeter,areaandvolume:Ccircle=2πR,Scircle=πR2,Crectangle=2(a+b),Srectangle=ab,Csquare=4a,

Ssquare=a2,Sring=π(R2-r2),Vcuboid=abc,Vcube=a3,Vcylinder=πR2h,Vcone=πR2h.

Thischapteristhecoreofalgebraandthefoundationofallalgebraicequations.Thecolorfulproblemsituationsandthejoyofsolvingproblemsareeasytoarousestudents'funinmathematics,sowemustpayattentiontoguidestudentstocarryouteffectivemathematicsactivitiesandcooperativeexchangesfromtheresearchofproblemsaroundthem,sothatstudentscanactivelystudyandexplorelearning.Intheprocessofgainingknowledge,improvingability,experiencingmathematicalthinkingmethods.

Chapter3PreliminaryUnderstandingofGraphics

Knowledgeframework

Themaincontentofthischapteristhepreliminaryunderstandingofgraphics.Startingwithfamiliarobjectsaroundlife,theunderstandingoftheshapeofobjectsgraduallyrisesfromsensibilitytoabstractgeometricfigures.Bylookingatthethree-dimensionalgraphicsandexpandingthethree-dimensionalgraphicsfromdifferentdirections,theinitialunderstandingofthethree-dimensionalgraphicsConnectionwithflatgraphics.Onthisbasis,recognizesomesimpleflatgraphics-straightlines,rays,linesegmentsandangles.Themathematicalideasinvolvedinthischapter:

1.Discussideasbycategory.Whendrawingstraightlinesatseveralpointsontheplane,youshouldpayattentiontodiscussingthesepoints;whendrawinggraphics,youshouldpayattentiontothevariouspossibilitiesofthegraphics.

2.Equationthinking.Whendealingwiththecalculationofthesizeoftheangleandthesizeofthelinesegment,itisoftennecessarytosolveitthroughthecolumnequation.

3.Graphictransformationideas.Whenstudyingtheconceptofangle,wemustfullyappreciatetheknowledgeoftherotationofrays.Whenprocessinggraphics,attentionshouldbepaidtotheapplicationoftransformationideas,suchastheconversionbetweenthree-dimensionalgraphicsandflatgraphics.

4.Turntothought.Whencountingstraightlines,linesegments,angles,andrelatedfigures,itshouldalwaysbeassignedtothespecificapplicationoftheformulan(n-1)/2.

Theseventhgrademathematics(below)knowledgepoints

Theseventhvolumeofthe7thgrademathematicsofthePeople'sEducationEditionmainlyincludesthesixchaptersofcollection,collationandexpressionofintersectinglinesandparallellines,planerectangularcoordinatesystems,triangles,binarylinearequations,inequalitiesandinequalitiesanddata.

Chapter5IntersectingLinesandParallelLines

1.KnowledgeFramework

Second,theconceptofknowledge

1.Adjacentcomplementaryangle:Amongthefourcornersformedbytheintersectionoftwostraightlines,twocornerswithacommonvertexandacommonsideareadjacentcomplementaryangles.

2.Oppositeangle:Thetwosidesofoneanglearetheoppositeextensionlinesoftheothercalledtwosides,andthetwoangleslikethisareoppositeeachother.

3.Verticalline:Whentwostraightlinesintersectatarightangle,theyarecalledperpendiculartoeachother,andoneofthemiscalledanotherperpendicularline.

4.Parallellines:Inthesameplane,twostraightlinesthatdonotintersectarecalledparallellines.

5.Co-locatedangle,internalstaggeredangle,co-locatedinternalangle:

Co-locatedangle:∠1and∠5likethispairofangleswiththesamepositionalrelationshiparecalledco-locatedangles.

Internalwrongangle:∠2and∠6Apairofangleslikethisiscalledinternalwrongangle.Ipsilateralinternalangle:∠2and∠5Apairofangleslikethisiscalledtheipsilateralinternalangle.

6.Proposition:Thesentencetojudgeathingiscalledaproposition.

7.Translation:Inaplane,agraphicismovedbyacertaindistanceinacertaindirection.Thismovementofthegraphiciscalledtranslationtranslation,ortranslationforshort.

8.Correspondingpoint:Eachpointinthenewfigureobtainedaftertranslationisobtainedbymovingacertainpointintheoriginalfigure.Suchtwopointsarecalledcorrespondingpoints.9.Theoremandnature

Thenatureoftheapexangle:theapexangleisequal.

Thenatureof10verticallines:

Property1:Thereisonlyonestraightlineperpendiculartotheknownstraightline.

Property2:Amongallthelinesegmentsconnectingapointoutsidethelineandeachpointontheline,theverticallinesegmentistheshortest.

11.Parallelaxiom:thereisonlyonestraightlineparalleltotheknownstraightlineafterpassing

astraightline.

CorollaryoftheParallelAxiom:Iftwostraightlinesareparalleltothethirdstraightline,thenthetwostraightlinesarealsoparalleltoeachother.

12.Thenatureofparallellines:

Property1:Thetwostraightlinesareparallelandtheangleofco-locationisequal.

Property2:Twostraightlinesareparallel,andtheinternalerroranglesareequal.

Property3:Thetwostraightlinesareparallelandcomplementarytotheinternalangle.

13.Determinationofparallellines:

Judgment1:Theco-locationangleisequal,andthetwostraightlinesareparallel.

Judgment2:Theinternalerroranglesareequal,andthetwostraightlinesareparallel.Judgment3:Theinternalangleisthesameastheside,andthetwostraightlinesareparallel.Thischapterenablesstudentstounderstandthetwopositionalrelationshipsbetweentwostraightlinesthatdonotcoincideintheplane,andtostudythecharacteristicsoftheangleformedwhenthetwostraightlinesintersect.Thecharacteristicsofthetwostraightlinesareperpendiculartoeachother,andthetwostraightlinesareparallelThelong-termcoexistenceconditionsandallofitscharacteristicsandthenatureofthetranslationaltransformationofgraphics,usingtranslationtodesignsomebeautifulpatterns.Keypoints:verticallinesandtheirproperties,parallellinejudgmentmethodsanditsproperties,translationanditsproperties,Andtheorganizationandapplicationofthese.Difficulties:Exploringtheconditionsandcharacteristicsofparallellines,thedifferencebetweentheconditionsandcharacteristicsofparallellines,usingtranslationpropertiestoexplorethetranslationrelationshipbetweengraphics,anddesigningpatterns.

Chapter6PlaneCartesianCoordinateSystem

One.Knowledgeframework

two.Knowledgeconcept

1.Orderednumberpair:Thepairconsistingoftwonumbersaandbinorderiscalledanorderednumberpairandiswrittenas(a,b)

2.Planerectangularcoordinatesystem:Intheplane,twonumberaxesperpendiculartoeachotherandhavingacommonoriginformaplanerectangularcoordinatesystem.

3.Horizontalaxis,verticalaxis,origin:thehorizontalnumberaxisiscalledthex-axisorthehorizontalaxis;theverticalnumberaxisiscalledthey-axisorthevertical