EDEXCEL A LEVEL FURTHER MATHS CORE PURE||VERIFIED ANSWERS||COMPLETE GUIDE

EDEXCEL A LEVEL FURTHER MATHS CORE
PURE||VERIFIED ANSWERS||COMPLETE GUIDE

Σ1 = ? (sigma 1)

ANS: n




Σ r = ? (sigma r from 1 to n)

ANS: 1/2n(n+1)




If the sum doesn't start from 1, sigma f(r) from k to n

ANS: sum/sigma from 1 to n - sum/sigma from 1 to k-1




Rearrange Σkf(r) from 1 to n

ANS: kΣf(r) from 1 to n




Σr^2 (sigma r squared)

ANS: 1/6n(n+1)(2n+1)




Σr^3 (sigma r cubed)

ANS: 1/4 n^2 (n+1)^2



rules for polynomials: ax^2 + bx + c = 0

roots α and β

,α + β = -b/a

αβ = c/a




rules for polynomials: ax^3 + bx^2 + cx + d = 0

roots α,β,γ

α + β + γ = -b/a

αβ+ αγ + βγ = c/a

αβγ = -d/a




rules for polynomials: ax^4 + bx^3 + cx^2 + dx + e = 0

roots α, β, γ, δ

α+β+γ+δ = -b/a

αβ+ αγ+ αδ+ βγ+ βδ+ γδ = c/a

αβγ + αβδ + αγδ + βγδ = -d/a

αβγδ = e/a




1/α + 1/β =

ANS: α+β/αβ




1/α + 1/β + 1/γ =

ANS: (αβ+αγ+βγ)/αβγ




1/α + 1/β + 1/γ + 1/δ =

ANS: (αβγ + αγδ + βγδ + αβδ) / αβγδ

, α^n x β^n =

ANS: (αβ) ^n




α^2 + β^2

ANS: (α+β)^2 - 2αβ




α^2 + β^2 + γ^2

ANS: (α+β+γ)^2 - 2(αβ+βγ+αγ)




α^2 + β^2 + γ^2 + δ^2

ANS: (α+β+γ+δ)^2 - 2(αβ+αγ+αδ+βδ+βγ+γδ)




α^3 + β^3

ANS: (α+β)^3 - 3αβ(α+β)




α^3 + β^3 + γ^3

ANS: (α+β+γ)^3 - 3(αβ+βγ+γα)(α+β+γ) +3αβγ




volume of revolution when y=f(x) is rotated around the x axis

ANS: volume = π∫y^2 dx

(pi integral of y squared dx)