S2 June 2015 Q6

Notes

NB: All powers of 1 must be simplified for the Accuracy(A) marks

M1: attempting to integrate \(x^n \to x^{n+1}\) and putting equal to 1, ignore limits

A1: correct integration

A1: \(k = n + 1\) Do not accept \(\dfrac{n + 1}{1^{n+1}}\)

Notes

M1: Writing or using \(\displaystyle\int_0^1 kx^{n+1}\,\mathrm{d}x\), ignore limits. Allow \(\displaystyle\int_0^1 kx(x)^n\,\mathrm{d}x\) Allow substitution of their \(k\)

A1: correct integration \(\dfrac{kx^{n+2}}{n + 2}\)

A1: correct answer only- must be in terms or \(n\)

Notes

M1: Attempting to integrate \(\displaystyle\int_0^1 kx^{n+2}\,\mathrm{d}x\), \(x^{n+2} \to x^{n+3}\), ignore limits. Do not allow substitution of \(k\) if it has \(x\) in it. This must be on its own with no extra bits added on.

A1: correct answer only

SC if they have \(\dfrac{k}{n + 2}\) as answer to part(b) award A1 for \(\dfrac{k}{n + 3}\)

Notes

M1: using “their(c)” − [“their(b)”]² with \(n = 2\) or correct Var(\(X\)) Using \(\displaystyle\int_0^1 kx^4\,\mathrm{d}x - \left[\int_0^1 kx^3\,\mathrm{d}x\right]^2\) for Var(\(X\))

M1: for writing or using 9 Var(\(X\)) or \(3^2\)Var(\(X\))

A1: cso