The charged particle transverse momentum (p(T)) spectra are presented for pp collisions at root s = 0.9 and 7 TeV. The data samples were collected with the CMS detector at the LHC and correspond to integrated luminosities of 231 mu b(-1) and 2.96 pb(-1), respectively. Calorimeter-based high-transverse-energy triggers are employed to enhance the statistical reach of the high-p(T) measurements. The results are compared with leading and next-to-leading order QCD and with an empirical scaling of measurements at different collision energies using the scaling variable x(T) equivalent to 2p(T)/root s over the p(T) range up to 200 GeV/e. Using a combination of xi, scaling and direct interpolation at fixed p(T), a reference transverse momentum spectrum at root s = 2.76 TeV is constructed, which can be used for studying high-p(T) particle suppression in the dense QCD medium produced in heavy-ion collisions at that centre-of-mass energy.