We discuss a method of calculating the key cosmological parameters on the basis of a selected scale factor by using exact solutions of the background equations. We specify the formulas for calculating the power spectrum, the spectral indices and their ratios, and the ratio of squared amplitudes of scalar and tensor perturbations. We obtain, for the first time, expressions for the basic cosmological parameters in terms of the scalar factor value at the instant of crossing the cosmological horizon. In this case, the cosmological parameters are calculated for a wide class of exact models. They are compared with their analogs derived in the slow-rolling approximation.