EDEXCEL A LEVEL FURTHER MATHS CORE PURE
Σ1m=m?m(sigmam1)m-m"ACCURATEmANSWER"mmmn
Σmrm=m?m(sigmamrmfromm1mtomn)m-m"ACCURATEmANSWER"mmm1/2n(n+1)
Ifmthemsummdoesn'tmstartmfromm1,msigmamf(r)mfrommkmtomnm-
m"ACCURATEmANSWER"mmmsum/sigmamfromm1mtomnm-msum/sigmamfromm1mtomk-1
RearrangemΣkf(r)mfromm1mtomnm-m"ACCURATEmANSWER"mmmkΣf(r)mfromm1mtomn
Σr^2m(sigmamrmsquared)m-m"ACCURATEmANSWER"mmm1/6n(n+1)(2n+1)
Σr^3m(sigmamrmcubed)m-m"ACCURATEmANSWER"mmm1/4mn^2m(n+1)^2
rulesmformpolynomials:max^2m+mbxm+mcm=m0m
rootsmαmandmβm-m"ACCURATEmANSWER"mmmαm+mβm=m-b/a
αβm=mc/a
rulesmformpolynomials:max^3m+mbx^2m+mcxm+mdm=m0
rootsmα,β,γm-m"ACCURATEmANSWER"mmmαm+mβm+mγm=m-b/a
αβ+mαγm+mβγm=mc/a
αβγm=m-d/a
rulesmformpolynomials:max^4m+mbx^3m+mcx^2m+mdxm+mem=m0m
rootsmα,mβ,mγ,mδm-m"ACCURATEmANSWER"mmmα+β+γ+δm=m-b/a
αβ+mαγ+mαδ+mβγ+mβδ+mγδm=mc/a
αβγm+mαβδm+mαγδm+mβγδm=m-d/a
αβγδm=me/a
1/αm+m1/βm=m-m"ACCURATEmANSWER"mmmα+β/αβ
1/αm+m1/βm+m1/γm=m-m"ACCURATEmANSWER"mmm(αβ+αγ+βγ)/αβγ
1/αm+m1/βm+m1/γm+m1/δm=m-
m"ACCURATEmANSWER"mmm(αβγm+mαγδm+mβγδm+mαβδ)m/mαβγδ
α^nmxmβ^nm=m-m"ACCURATEmANSWER"mmm(αβ)m^n
α^2m+mβ^2m-m"ACCURATEmANSWER"mmm(α+β)^2m-m2αβ
α^2m+mβ^2m+mγ^2m-m"ACCURATEmANSWER"mmm(α+β+γ)^2m-m2(αβ+βγ+αγ)
α^2m+mβ^2m+mγ^2m+mδ^2m-m"ACCURATEmANSWER"mmm(α+β+γ+δ)^2m-
m2(αβ+αγ+αδ+βδ+βγ+γδ)
α^3m+mβ^3m-m"ACCURATEmANSWER"mmm(α+β)^3m-m3αβ(α+β)
α^3m+mβ^3m+mγ^3m-m"ACCURATEmANSWER"mmm(α+β+γ)^3m-m3(αβ+βγ+γα)(α+β+γ)m+3αβγ
volumemofmrevolutionmwhenmy=f(x)mismrotatedmaroundmthemxmaxism-
m"ACCURATEmANSWER"mmmvolumem=mπ∫y^2mdxm
(pimintegralmofmymsquaredmdx)
, volumemofmrevolutionmwhenmym=mf(x)mismrotatedmaroundmthemymaxism-
m"ACCURATEmANSWER"mmmπ∫x^2mdym
(pimintegralmofmxmsquaredmdy)
volumemofmamcylinderm-m"ACCURATEmANSWER"mmmπr^2h
volumemofmamconem-m"ACCURATEmANSWER"mmm1/3πr^2h
whatmismammatrix?m-
m"ACCURATEmANSWER"mmmammatrixmismanmarraymofmelementsmsetmoutminmampairmofmb
rackets)
whatmismamsquaremmatrix?m-
m"ACCURATEmANSWER"mmmsamemnumbermofmrowsmasmcolumns
Whatmismamzerommatrix?m-
m"ACCURATEmANSWER"mmmAmmatrixmwheremallmthemelementsmarem0
Whatmismanmidentitymmatrix?m-
m"ACCURATEmANSWER"mmmAmmatrixmwhichmcontainsm1smandm0s
Whatmismthem2mxm2midentitymmatrix?m-m"ACCURATEmANSWER"mmm1m0m
0m1
whatmismthem3mxm3midentitymmatrix?m-m"ACCURATEmANSWER"mmm1m0m0m
0m1m0m
0m0m1
howmdomyoumaddmormsubtractmmatrixes?m-
m"ACCURATEmANSWER"mmmadd/msubtractmcorrespondingmelements
howmdomyoummultiplymammatrixmbymamscalarm-
m"ACCURATEmANSWER"mmmmultiplymeachmelementmbymthemscalar
Howmdomyoummultiplymmatrices?m
ambmemf
cmdmxmgmhm-m"ACCURATEmANSWER"mmmaem+mbg.maf+mbhm
ce+mdgmcf+mdh
whatmismthemdeterminantmofmam2mxm2mmatrix?
amb
cmdm-m"ACCURATEmANSWER"mmmadm-mbc
Whatmismthemdeterminantmofmam3mxm3mmatrix?m
ambmcm
dmemfm
gmhmim-m"ACCURATEmANSWER"mmmam(meim-mfh)m-mb(dim-mfg)m+mc(dhm-meg)
whatmismtheminversemofmammatrix?m-
m"ACCURATEmANSWER"mmmthemmatrixmsuchmthatmM(Mminverse)m=mI
whatmismtheminversemofmmatrixm
ambm
cmdm-m"ACCURATEmANSWER"mmm(1/detM)mdm-bm
Σ1m=m?m(sigmam1)m-m"ACCURATEmANSWER"mmmn
Σmrm=m?m(sigmamrmfromm1mtomn)m-m"ACCURATEmANSWER"mmm1/2n(n+1)
Ifmthemsummdoesn'tmstartmfromm1,msigmamf(r)mfrommkmtomnm-
m"ACCURATEmANSWER"mmmsum/sigmamfromm1mtomnm-msum/sigmamfromm1mtomk-1
RearrangemΣkf(r)mfromm1mtomnm-m"ACCURATEmANSWER"mmmkΣf(r)mfromm1mtomn
Σr^2m(sigmamrmsquared)m-m"ACCURATEmANSWER"mmm1/6n(n+1)(2n+1)
Σr^3m(sigmamrmcubed)m-m"ACCURATEmANSWER"mmm1/4mn^2m(n+1)^2
rulesmformpolynomials:max^2m+mbxm+mcm=m0m
rootsmαmandmβm-m"ACCURATEmANSWER"mmmαm+mβm=m-b/a
αβm=mc/a
rulesmformpolynomials:max^3m+mbx^2m+mcxm+mdm=m0
rootsmα,β,γm-m"ACCURATEmANSWER"mmmαm+mβm+mγm=m-b/a
αβ+mαγm+mβγm=mc/a
αβγm=m-d/a
rulesmformpolynomials:max^4m+mbx^3m+mcx^2m+mdxm+mem=m0m
rootsmα,mβ,mγ,mδm-m"ACCURATEmANSWER"mmmα+β+γ+δm=m-b/a
αβ+mαγ+mαδ+mβγ+mβδ+mγδm=mc/a
αβγm+mαβδm+mαγδm+mβγδm=m-d/a
αβγδm=me/a
1/αm+m1/βm=m-m"ACCURATEmANSWER"mmmα+β/αβ
1/αm+m1/βm+m1/γm=m-m"ACCURATEmANSWER"mmm(αβ+αγ+βγ)/αβγ
1/αm+m1/βm+m1/γm+m1/δm=m-
m"ACCURATEmANSWER"mmm(αβγm+mαγδm+mβγδm+mαβδ)m/mαβγδ
α^nmxmβ^nm=m-m"ACCURATEmANSWER"mmm(αβ)m^n
α^2m+mβ^2m-m"ACCURATEmANSWER"mmm(α+β)^2m-m2αβ
α^2m+mβ^2m+mγ^2m-m"ACCURATEmANSWER"mmm(α+β+γ)^2m-m2(αβ+βγ+αγ)
α^2m+mβ^2m+mγ^2m+mδ^2m-m"ACCURATEmANSWER"mmm(α+β+γ+δ)^2m-
m2(αβ+αγ+αδ+βδ+βγ+γδ)
α^3m+mβ^3m-m"ACCURATEmANSWER"mmm(α+β)^3m-m3αβ(α+β)
α^3m+mβ^3m+mγ^3m-m"ACCURATEmANSWER"mmm(α+β+γ)^3m-m3(αβ+βγ+γα)(α+β+γ)m+3αβγ
volumemofmrevolutionmwhenmy=f(x)mismrotatedmaroundmthemxmaxism-
m"ACCURATEmANSWER"mmmvolumem=mπ∫y^2mdxm
(pimintegralmofmymsquaredmdx)
, volumemofmrevolutionmwhenmym=mf(x)mismrotatedmaroundmthemymaxism-
m"ACCURATEmANSWER"mmmπ∫x^2mdym
(pimintegralmofmxmsquaredmdy)
volumemofmamcylinderm-m"ACCURATEmANSWER"mmmπr^2h
volumemofmamconem-m"ACCURATEmANSWER"mmm1/3πr^2h
whatmismammatrix?m-
m"ACCURATEmANSWER"mmmammatrixmismanmarraymofmelementsmsetmoutminmampairmofmb
rackets)
whatmismamsquaremmatrix?m-
m"ACCURATEmANSWER"mmmsamemnumbermofmrowsmasmcolumns
Whatmismamzerommatrix?m-
m"ACCURATEmANSWER"mmmAmmatrixmwheremallmthemelementsmarem0
Whatmismanmidentitymmatrix?m-
m"ACCURATEmANSWER"mmmAmmatrixmwhichmcontainsm1smandm0s
Whatmismthem2mxm2midentitymmatrix?m-m"ACCURATEmANSWER"mmm1m0m
0m1
whatmismthem3mxm3midentitymmatrix?m-m"ACCURATEmANSWER"mmm1m0m0m
0m1m0m
0m0m1
howmdomyoumaddmormsubtractmmatrixes?m-
m"ACCURATEmANSWER"mmmadd/msubtractmcorrespondingmelements
howmdomyoummultiplymammatrixmbymamscalarm-
m"ACCURATEmANSWER"mmmmultiplymeachmelementmbymthemscalar
Howmdomyoummultiplymmatrices?m
ambmemf
cmdmxmgmhm-m"ACCURATEmANSWER"mmmaem+mbg.maf+mbhm
ce+mdgmcf+mdh
whatmismthemdeterminantmofmam2mxm2mmatrix?
amb
cmdm-m"ACCURATEmANSWER"mmmadm-mbc
Whatmismthemdeterminantmofmam3mxm3mmatrix?m
ambmcm
dmemfm
gmhmim-m"ACCURATEmANSWER"mmmam(meim-mfh)m-mb(dim-mfg)m+mc(dhm-meg)
whatmismtheminversemofmammatrix?m-
m"ACCURATEmANSWER"mmmthemmatrixmsuchmthatmM(Mminverse)m=mI
whatmismtheminversemofmmatrixm
ambm
cmdm-m"ACCURATEmANSWER"mmm(1/detM)mdm-bm
