On F-pure thresholds and quasi-F-purity of hypersurfaces

We show that quasi-$F$-pure but not $F$-pure isolated quasi-homogeneous hypersurface singularities necessarily have $F$-pure threshold $1-\frac{1}{p}$. This extends work of Bhatt and Singh beyond the Calabi-Yau case. We also classify the (quasi)-$F$-purity of Fermat hypersurfaces.