  Conjugate points play an important role in the proofs of the singularity
theorems of Hawking and Penrose. We examine the relation between singularities
and conjugate points in FLRW spacetimes with a singularity. In particular we
prove a theorem that when a non-comoving, non-spacelike geodesic in a singular
FLRW spacetime obeys conditions (39) and (40), every point on that geodesic is
part of a pair of conjugate points. The proof is based on the Raychaudhuri
equation. We find that the theorem is applicable to all non-comoving,
non-spacelike geodesics in FLRW spacetimes with non-negative spatial curvature
and scale factors that near the singularity have power law behavior or power
law behavior times a logarithm. When the spatial curvature is negative, the
theorem is applicable to a subset of these spacetimes.
