  We introduce the notion of right pre-resolutions (quasi-resolutions) for
noncommutative isolated singularities, which is a weaker version of
quasi-resolutions introduced by Qin-Wang-Zhang. We prove that right
quasi-resolutions for noetherian bounded below and locally finite graded
algebra with right injective dimension 2 are always Morita equivalent. When we
restrict to noncommutative quadric hypersurfaces, we prove that a
noncommutative quadric hypersurface, which is a noncommutative isolated
singularity, always admits a right pre-resolution. Besides, we provide a method
to verify whether a noncommutative quadric hypersurface is an isolated
singularity. An example of noncommutative quadric hypersurfaces with detailed
computations of indecomposable maximal Cohen-Macaulay modules and right
pre-resolutions is included as well.
