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Uncertainties on centralmixing inmain-sequence (MS) and coreHe-burning (He-B) phases affect key predictions of stellar evolution such as late evolutionary phases, chemical enrichment, ages, etc.We propose a test of the extension of extra-mixing in two relevant evolutionary phases based on period spacing (ΔP) of solar-like oscillating giants. From stellar models and their corresponding adiabatic frequencies (respectively, computed with ATON and LOSC codes), we provide the first predictions of the observable ΔP for stars in the red giant branch and in the red clump (RC).We find (1) a clear correlation between ΔP and the mass of the helium core (MHe); the latter in intermediatemass stars depends on the MS overshooting, and hence it can be used to set constraints on extra-mixing during MS when coupled with chemical composition; and (2) a linear dependence of the average value of the asymptotic period spacing (ΔPa) on the size of the convective core during the He-B phase. A first comparison with the inferred asymptotic period spacing for Kepler RC stars also suggests the need for extra-mixing during this phase, as evinced from other observational facts. [ABSTRACT FROM AUTHOR]