高中数学双语教案.docx

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高中数学双语教案.docx

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高中数学双语教案.docx

高中数学双语教案

§1Arithmetic算术

Thenumbers0,1,2,3……arecalledwholenumbersorintegers.So23isanintegerbut1.5isnotaninteger.

Anumbergreaterthanzeroiscalledapositivenumber.

Anumbersmallerthanzeroiscalledanegativenumber.

0isanintegerbutitisneitherpositivenornegative.

Anintegerthatisdivisibleby2isaneveninteger.Anintegerthatisnotdivisibleby2isanoddinteger.

Foranytwonumbersonthenumberline,thenumberontheleftislessthanthenumberontheright,forexample,2<3and-4<-3.

Theabsolutevalueofanumberistheequivalentpositivevalue.

|+2|=+2,|-3|=+3

Ifxisanintegerdivisiblebyanotherintegery,thenxissaidtobeeamultipleofy,andyissaidtobeafactorordivisorofx.

Thefactorsof12are:

1,2,3,4,6,12.

Themultipleof5are:

5,10,15,20……

Ifpisawholenumberwhichhasnootherfactorsbesidesitselfand1,pisaprimenumber.2,3,5,7,11,…areprimenumbers.But1isnotconsideredaprimenumber.

Theleastcommonmultipleoftwonumbersisthesmallestnumberwhichisacommonmultipleofbothnumbers.

Afractionisanumberwhichrepresentsaratioordivisionoftwonumbers.Afractioniswrittenintheform

.Thenumberonthetop,a,iscalledthenumerator;thenumberonthebottom,b,iscalledthedenominator.

Afractioncannothave0asadenominator,sincedivisionby0isnotdefined.

Tocomparethevaluesoftwofractions.Is

greaterorlessthan

Firstmultiply4by9andget36;thenmultiply5by7andget35,asshownhere:

364535

Since36isgreaterthan35,

isgreaterthan

.（Itisnotnecessarytomultiply7by9asthecommondenominator.）

Adecimalfractionisafractionwhosedenominatorissomepowerof10（suchas10,100,1000ete.）

Thedigitsofanumberarenamedasfollows:

2,078.146

千百十个十百千

位位位位分分分

数数数数位位位

数数数

thousands’digit千位数

hundreds’digit百位数

tens’digit十位数

units’digit个位数

tenths’digit十分位数

hundredths’digit百分位数

thousandths’digit千分位数

Roundingoffnumberscanhelpyougetquick,approximateanswers.Examples:

Roundoff538,423.98tothenearesthundred.Theansweris538,400.

Roundoff24.76tothenearesttenth.Theansweris24.8.

Thepartsofadivisionproblemareindicatedintheexamplebelow.

Thequotientis5

Theaverageorarithmeticmeanof12,3,6is:

（12+3+6）÷3=7.

Ifagroupofnumbersisarrangedinorder,themiddlenumberiscalledthemedian.

Tofindthemedianof12,3,6,arrangetheminorder:

3,6,12.Themedianis6.

Ifthenumberofitemsinthegroupiseven,themedianistheaverageofthetwomiddlenumbers.Forexample,tofindthemedianof6,3,30,14,arrangetheminorder:

3,6,14,30.Themedianis（6+14）÷2=10.

Ingeneral,themedianandtheaverageofacollectionofnumbersaredifferent.

Powers,Exponents,andRoots:

Ifbisanynumberandnisawholenumbergreaterthan0,b

meantheproductofnfactorseachofwhichisequaltob.Thus,b

=b*b*b*…*b,wheretherearencopiesofb.

Theexpressionb

iscalledthenthpowerofb,niscalledtheexponent;biscalledthebase.

Anoddintegerpowerofanegativenumberisnegative,andanevenintegerpowerofanegativenumberispositive.Forexample,（-2）

=-8,but（-2）

=16.

Youshouldknowthefollowinglaws:

=1（b≠0）

（b≠0）

Ifyouraiseanumberdtothenthpowerandtheresultisb,thendiscalledthenthrootofb.

Noticethefollowingrelations:

Exercise

1.AllthefollowingnumbersarepositiveEXCEPT

（A）5.3（B）0.07（C）0（D）2（E）5

2.Thenumberofthefactorsof24is

（A）9（B）8（C）7（D）6（E）5

3.Thedistinctprimefactorsof24are

（A）1,2,3（B）2,3（C）2,3,6（D）8,3

4.Howmanyofthepositiveintegerslessthan25areintegermultiplesof4?

（A）7（B）6（C）5（D）4（E）3

5.Theleastcommondenominatorof

and

（A）

（B）

（C）

（D）48（E）96

6.Thetenths’digitof3,610.48is

（A）3（B）6（C）1（D）4（E）8

7.Theunits’digitof5

（A）20（B）10（C）5（D）4（E）0

8.Round508.64tothenearesttenth.Theresultis

（A）510（B）508（C）508.6（D）508.7（E）509

9.360dividedby37,theremainderis

（A）27（B）333（C）0（D）9（E）

10.Theaverageorarithmeticmeanof2,4,6,10is

（A）6（B）5（C）5.5（D）4（E）3

11.Themedianof2,4,6,10is

（A）6（B）5（C）5.5（D）4（E）3

12.10

÷10

（A）100（B）10（C）0.1（D）0.01（E）-2

13.If87million=8.7*10

thenn=

（A）5（B）6（C）7（D）8（E）9

14.

（A）

（B）5

（C）3

（D）15

（E）3

15.Whichofthefollowinghasthegreatestvalue?

（A）

（B）0.3（C）0.01п（D）

（E）

16.7lessthan5x.Thismeans

（A）7-5x（B）5x-7（C）7<5x（D）7>5x（E）7-5+x

17.8islessthan2y.Thismeans

（A）8-2y（B）2y-8（C）8<2y（D）2y<8（E）8-2+y

§2Algebra代数

Thelettersinanalgebraicexpressionarecalledvariablesorunknowns.Whenavariableismultipliedbyanumber,thenumberiscalledthecoefficientofthevariable.Thus,intheexpression3x

-5y,thecoefficientofx

is3,andthecoefficientofyis–5.

Theonlyalgebraictermswhichcanbeaddedendsubtractedareliketerms.Forexample,2x

+3x-5x

=-3x

+3x.

Anequationisastatementthatsaystwoalgebraicexpressionsareequal.

Alinearequationoranequationofthefirstdegreeisoneinwhichvariablesareraisedonlytothefirstpower.Forexample,2x+3=9.

Aquadraticequationisanequationwhichcontainssquaresoftheunknownaswellastermsofthefirstdegree.Forexample,3x

+2x-4=0,x

-9=0。

Youcansolveaquadraticequationbyfactoring.

Aratioisacomparisonoftwonumbersbydivision.Theratioofatobiswrittenasa:

bor

Aproportionisastatementthattworatiosareequal.Forexample,2:

3=10:

15,or

Intheproportiona:

b=c:

d,thetermsontheoutside（aandd）arecalledtheextremes,andthetermsontheinside（bandc）arecalledthemeans.

Twovariables,aandb,aredirectlyproportional,iftheysatisfyarelationshipoftheforma=kb,wherekisanumber.

Twovariables,aandb,areindirectlyproportional,iftheysatisfyarelationshipoftheformab=k,wherekisanumber.

Sometimestheword“directly”isomitted.So“aandbareproportional”means:

aandbaredirectlyproportional.

Aninequalityisastatementthatoneexpressionisnotequaltoanother.

Tofindthesolutionsetforaninequality,youmustremembertheseprinciples.

1.Youcanaddthesamequantitytoorsubtractthesamequantityfrombothsidesofaninequalitywithoutalteringitssolutionset.

If5>3,then5+2>3+2.If5>3,then5-4>3-4.

2.Youcanmultiplyordividebothsidesofaninequalitybythesamenegativequantitywithoutalteringitssolutionset,youmustchangethedirectionoftheinequality.

Iif5>3,then5（-2）<3（-2）.If5>3,then

Exercise

1.Weknowthat

≠-3.If

theny=

（A）+3only（B）–3only（C）+9only（D）–9only（E）+3or-3

2.IfP=EI,andE=IR,findPintermsofEandR.

3.If5x+2<2x+5,thenallofthefollowingmaybeavalueofxEXCEPT

（A）0（B）1（C）–1（D）–2

4.Abagofchickenfeedwillfeed18chickensfor54days.Forhowmanydayswillitfeed12chickens?

（A）36（B）38（C）54（D）72（E）81

5.7x-5y=13;2x-7y=m26;9x-12y=?

（A）13（B）26C）39（D）42（E）52

6.Howmanysolutionsdoestheequationa-3=

have?

（A）0（B）1（C）2（D）3（E）4

What’stheChineseforthefollowingword?

1.integer__________2.numerator__________3.roundoff__________4.decimal__________5.fraction__________6.positive__________7.multiple__________8.power__________9.remainder__________10.median__________11.denominator__________12.oddinteger__________13.exponent__________14.arithmeticmean__________15.quotient__________16.primenumber__________17.absolutevalue__________18.divisor__________19.negative__________20.root__________

Howtodescribe“

”___________________________“

”_______________

§Geometry

Anacuteanglehasameasuregreaterthan0°butlessthan90°.

Arightanglehasameasureof90°.

Anobtuseanglehasameasuregreaterthan90°butlessthan180°

Astraightangle（whichlookslikeastraightline）hasameasureof180°.

Twoanglesthattogetherhaveameasureof90°arecalledcomplementaryangles.

Twoanglesthattogetherhaveameasureof180°（thatis,twoanglesthattogetherformastraightline）arecalledsupplementaryangles.

Iftwolinesintersect,thefouranglesformedareeitherequalorsupplementary.Theanglesoppositeoneanotherarecalledverticalanglesandareequal.Theanglesnexttooneanotheraresupplementary.

Iftwoparallellinesareintersectedbyathirdline,calledatransversal,theeightanglesformedareeitherequalorsupplementary.

Inthefigure,linePQisparalleltolineRS.

Thenangles1and2arecalledcorrespondinganglesandareequal.

Angles2and3arecalledalternateinterioranglesandareequal.

Atrianglethathastwoequalsidesiscalledanisoscelestriangle.

Ifallthreesidesofatrianglearethesamelength,thetriangleiscalledanequilateraltriangle.

Thesumofthemeasuresofthethreeinterioranglesofatriangleis180°.

Ifthevertexofanangleisatthecenterofacircle,thentheangleiscalledacentralangleanditsmeasureisequaltothemeasureofthearcitintercepts.

Ifthevertexofanangleliesonacircle,thentheangleiscalledaninscribedangleinthecircleanditsmeasureisequaltohalfthemeasureofthearcitintercepts.

IncircleO,angle

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