We analyze low-energy scattering of positrons on Ar atoms and N2 molecules using Modified Effective-Range Theory (MERT) developped by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. We use formulation of MERT based on exact solutions of Schrödinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes well experimental data, provided that effective-range expansion is performed both for s-and p-wave scattering, which dominate in the considered regime of positron energies (0.4 -2 eV). We estimate the values of the s-wave scattering lenght and the effective range for e + -Ar and e + -N2 collisions.Electron (and positron) scattering on atoms at very low energies is dominated by polarization forces. Applicability of MERT to low-energy positron scattering was already hypothesized in [2]. However, first measurements of total cross sections for positron scattering at low energies on noble atoms come only from seventies [10,11].The most systematic data for noble atoms, extending down to 0.3 eV were done in WSU Detroit lab, using positrons from a short-lived C 11 radionuclid, with about 0.1 eV energy resolution [11]. Those data indicated clearly a rise of the cross section in the zero energy limit in gases, like He, Ar, H 2 , Kr, Xe, CO 2 , see [11]. Unfortunately, subsequent experiments [12, 13] used Ne 22 source and thick W-vanes positron moderator, thus worsening energy resolution and not allowing to make reliable measurements below 1 eV. To gain in signal, large apertures and strong guiding magnetic fields were used, leading to underestimation of cross sections -some data showed even a fall in the limit of zero energy for highly polarizable targets, like C 6 H 6 [14].Only two of the most recent set-ups reached energies below 1 eV with good signal-to-noise ratio. In San Diego annihilation rates in Ar and Xe were measured, showing a steep rise below 1 eV [15]. In Trento total cross sections in Ar and N 2 were measured [16] with angular resolution better by a factor of 30 than in some previous experiments [12]. Both laboratories confirm the early observations from WSU Detroit on the rise of positron cross sections in the zero-energy limit. Such a rise is also predicted by ab-initio theories [17], see [16] for detailed comparison. A phenomenological attempt to apply MERT-like fit for low-energy cross sections in benzene and cyclohexane was done by Karwasz, Pliszka and Zecca [18].In the present paper we apply MERT to positron total cross sections on argon and nitrogen, using recent experimental data from Trento [16]. We use MERT model based on direct solution of Schrödinger equation with polarization potential as originally proposed by O'Malley, Spruch and Rosenberg [1]. Differently from earlier works, for the p-wave phaseshift we consider not only the polarization potential but contribution from a general-type short range interaction. This allows us to extend the MERT applicability for positrons to energies above 1 e...