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A-Level:核心数学CoreMaths,力学数学,统计数学,决策数学
CoreMathematics1(AS/A2)-----核心数学1
1Algebraandfunctions-----代数和函数
2Quadraticfunctions-----二次函数
3Equationsandinequalities---等式和不等式
4Sketchingcurves---画图(草图)
5Coordinategeometryinthe(x,y)plane--------平面坐标系中的坐标几何
6Sequencesandseries——数列
7
Differentiation------微分
------积分
每章内容:
1Algebraandfutictlons
Simplifyinganexpressionbycollectingliketerms
L3Expandinganexpressiono
1用Factorhinganexpression
IS
Factorisingaquadr^kexpression
L6Thvlas\sofindicesfordllrationalexponents
L7Theuseandnianipulationofitrds
io
L8Rationalisingtheiknonnridtorofafractionivhen才二dw:
Summaryofkeypoinis
Quadraticfunctions2A14
XCxs
Plottingthes^phsofSolving
】“沪巧Completing15
Ebyractorisati
:Solvingquddratiu
映>;肯『
“
cequtijLArbycomgTfctjngth」square.''Juiht^muh
>J20
;
Summaryofkfy尸為Quadraticformulae
24
Equations匚M
25
Solvingsin
^ncc^*bysubstitutinn
Solvingsimultaneob.
UsingsubstI
33
SolvinglinGi『in何亦It華&
3J2b
^^^ii^s
Suiiunaryof匕叮心疋试
Sketching<\3S
$ofcubicfunctions丽
^lW^yaphsnfcubkfuiKtioiu
Sketchinutilereciprocalfunction
■
ttivinicrsectionpointsofo[functionstosolv<equations
(x+⑷dnd冃工-川
舉effectofthetransforiiiationsfiux)and
'Fftrfotmingtransformationsonthesketchesofcurves
詁ryofkeypoints
b4
5Coordinategeonwtryinthe(x9y)plane6S
=nix+corax+如+c=065
-y严ifi(x-心)7&
'75
Summaryofkeypoints
6Sequencesandseries
\//()85
\C/^\°°
」97
Summaryofkeypoints'〃丿)101
7Differentiation(//.102
7」Thederivativeoff(x)asthethiCpn^ktotft^graphy=f(x)102
105
109
113
114
115
116
117
121
122
122
124
125
126
128
130
CoreMathematics2(AS/A2)核心数学2
----代数和函数
正弦和余弦定理
----
----指数和对数
(x,y)plane--------平面坐标系中的坐标几何
---二项展开式
---弧度制及其应用
---等比数歹U
----三角函数的图形
------微分
------三角恒等式和简单的三角等式
----积分
每章内容:
AigcbrjdEidluiKtions1J
13polynomialby(xip)5
UsingtheRemainderTheorem13
Summaryofk(?ypoints17
:
Thesintandcosinerule18
2AUsingthesineruletofindmissingsidesUsing18
^wnanglesTheruleand21
23findingtwow*foranih^FEo23
#切Mckssing24
27
^ic^
«30
.■#4RIle3nr<!'『庶耳竝遁Theo32
rem36
Suniinjjyofkeypolrt1
ot^Jy^ngleus)闵j
37
tns
Exponctuiahan<r^ogaMh*37
Th<bfunctk严Writingnsasa
3J39
Calculating*丄耳to
王4()
2LawsofJogarithmS
玉341
Solvingequations汐a'-b
Changingthemt
Summaryofkeypoints
49
Ck49
Coordinateniotinlinethe(x,y\plant
A57
60
4*
68
iriomTalexpansionstriangle70
XCombinntionsandfactorial70
Using(:)mthebinomialexpansion72
5-4Expanding(d+bxYrusingthebinomialexpansion73
Summaryofkeypoint*
75
79
oKaaianmeasureanaitsapplicationsUsingradianstomeasureanglesThelengthof
61thearcofacircleTheareaofasectorofacircleTheareaofasegmentofa
Summaryofkeypoints93
Geometricsequencesandseries94
Summaryofkeypoints109
geometricsequencestosolveproblemsThesumofageometricseries
110
Thesumtoinfinityofa
geometricseries
functions
&5121
Sine,cosineand
SummaryofkeypoE;'tangent127
(unctions129
Thevaluesoftrigonomef/functionsinthe129
Exactvaluesandsurdsf131
Graphsofsine0fcosJJ、
ms135
Simpletransformantso
140
Differentiationleequationstitlesometricalequationseform141
Simpletrigosin(nd+a),cos(n0+a)andtan(n0+a)=kig?nometrical141
Solvingsimjequations146
Solvingeqy149
Solvingqud151
156
11Integratio・157
、,minipjumandpointsofinflexion
^rninjfpointsto
亠
“inis164
169
Trigonom^/Jidentitie
10177
】
Summaryo
teintegration
acurve
acurvethatgivesnegativevaluesnastraightlineandacurverapeziumRule
ofkeypoints
11
CoreMathematics3(AS/A2)核心数学3
1Algebrafractions------分式代数
2Functions-----函数
3Theexponentialandlogfunctions指数函数和对数函数
4Numericalmethod------数值法
5Transforminggraphoffunctions-------函数的图形变换
6Trigonometry-----三角
7Furthertrigonometricandtheirapplications------高级三角恒等式及其应用
8Differentiation------微分
每章内容:
AlxvbrditIriiciions
^
LUI1{.CILUI^口
->
Inxalxvbriiitfr*^jindtiirrcn)i»iii<lvrLtit.-^in
2Erunctioi-i^
2,1Mappingdiingrarnsand耳ofopaeiiitions(J
-tions<iridfunctioiinotatk>ti
2-3Range,mappingdiagrams,,graphsanddefinitions
J
Usingcompositefunctions#*f丿
Findingandusinginverse-
Theexponentialandlogfunetions°
3/1Introdticingexponent・ialrtionsoflheI'omCj^・h立Graphsofexponential
t<lny4-cnU>iTi耳$[J
旷卞:」^前m扌匸卩存占;逆"二tlxfn琴,严
U^irig^Eidinwub©■—CXJJ€»TLOkltkJIfLIIlC'Flori
护主亠二亠亠」一■■
Numericalmethod?iir^^of”<>gr^jj^/ica11y
「____2=」cth^Js^lcrlindapproximateroot萤
^ingileratialgebraiciiicthi^irs'lw^nndapproximatert>ots
of陶仟彳l
Tran露Fermi订呂graf^/offui^ctiini^
5-1Sketch!tiggraphsot1^hhockx!^^4^uy一netlf(x)lion5u2Sketchingg^r^phsy=f(lxl)
(Apolvin^amcxluliismictionstosketch?«什erv«fih订花JJCFIMH11台Mliellinglheco-ordinatesof
given
AjipJyingacorn^ixiatj
H,Sketchingcosecant仇andtrar^cotaingEfU丹f^tant也cosecant优andcotangent甘xpressicmsjproving
iclentiti^iindsolvingequations,using
I'rigonomctry
64Thefijnr/Q?6?/
Simplifying£sec他cowO?RandcotH
idcnlitles十llan2^=$2Hand1+cot-^=cosec2
7..FurthertngimonietrkidentitiesandtheifappliesHons
St/LMrigadditiontrigoiionietricallormulac
二Usingdoublean^lctrigoiiDmctricalfarmulae
7?TSolvingequdtiomandprovingIdcntltiicsusingdoubkiiriglefoniiuLie^^74101
Usin^
'hcracloitbrinuiai'112
8Differentiation
&ingthechainrule
K4Iifferentiatjngtheexponentialfunction
Differentiating5inx(C~128
Differentiatingxcos130
131
Differentistin^t^nx
132
DifferenliatkngfurthertrigonometrLcaJfunctions
[differentiatingfunctiansformedbycombining九丁frigon贰#乎卜cxprtncniiaL
logfkritl-imLcandpolynomialfLinctior^;
CoreMathematics3(AS/A2)核心数学4
CoreMathematics3(AS/A2)核心数学5
1Partialfractions----部分分式
2Coordinategeometryinthe(x,y)plane平面坐标系中的坐标几何
3Thebinomialexpansion---二项展开式
4Differentiation------微分
5Vectors-----向量
------积分
每章内容:
AIXJULLl||\ULHJKUMII^VtXUMlIUUtSUilWJ-^JJJLSI;
In2or3dimensions二,二二55
1PartialfractionsLCartesiantoniponeidiGfa\yytorin2
Addingandsubtractingalgehraicdimensions56
fractionsCartesiancomponentsol
Partialfractionswithtwolinearin3dimensio%7^;
factorsinthedenominatorvector
Extending2/悸幺?冲
Partialfractionswithttneeormor^62
linearfactorsinth<?denominator3resultsiooftwovectorsn64
Partialtractionswithrepeatedlinear]heseal;|ofastraight
factorsinthedenominatorImproperThevect*70
fractionsintopartialfractions
戸理逖石
[nUT^clrnjfetraighilinevector74
kF
Jobetweentwostraight
2Cootdinategeometryinthe(x,y)2」
ParametricParametricequationsequationsusedusedtotodtiinexlines
theuxirdin^tesotaUsingparanictrk:y1fi2
equ訓UKndinate驴oimtr*■jitrgrating£t^ndardJunctions«2
Convertingparamet^.jitionsinto11Integratingusingthereversechain
cartesian世qiut档才FindingtheruleB4
Usingtrigonometricidentitiesin
itrea^iidcheairvegivenbypannr严
2Aintegration
旷
^quationsUsingpartialfractionsto
3FhebinomialexIntegrateexpressions
3,iUsingstandardpatternstointegrdle
Thebinomialexpulsiona-positiveexpre^
integralindexUsingthebinomid21IntegrationbypartsNumerical
+l^x)"\j'integrationIntegrationtofindateas
andvolumes
Usingpartialfracti>#w$Kjtwtiiv■
331Usingintegrationtosolve
binamiaiexpanjy^f\、differentialequationsDifkrtntiai
rquatjomincontext
DifferentlaUon
10ft
(Inti;onsgiven
6J1
pararnetricaifrf/11
42Diffenyitiating^uationwhicharcimplicit1
OExamstylepaper
43Diffett»y^a!ingthefunctiona1
{垃tSftitiibnandratesofchangeFormulaeyouneedtoknow
Listofsymbolsandnotation126
5VecS^?<^54,Ve?tord^fmitipns4ndvector
^^iiAgrams
Answers
r、§,2Vectorarithmeticandtheunitvector
SIIndex139