A symmetric density and calibrated readings

A continuous random variable X has density f(x)=kx(1-x) for 0 <= x 1, and zero elsewhere, where k>0. A calibrated reading is R=8+4X. - Find k and verify non-negativity of the density on its support. - Find the median and the mode of X, giving a reason for each. - Calculate E(X) and Var(X). - Find E(R), Var(R), and P(R>11).