EDEXCEL A LEVEL FURTHER CORE PURE MATHS

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