  Solar-like oscillations are expected to be excited in stars of up to about
1.6 solar masses. Most of these stars will have convective cores during their
Main-sequence evolution. At the edges of these convective cores there is a
rapid variation in the sound speed which influences the frequencies of acoustic
oscillations. In this paper we build on earlier work by Cunha and Metcalfe, to
investigate further the impact that these rapid structural variations have on
different p-mode frequency combinations, involving modes of low degree. In
particular, we adopt a different expression to describe the sound speed
variation at the edge of the core, which we show to reproduce more closely the
profiles derived from the equilibrium models. We analyse the impact of this
change on the frequency perturbation derived for radial modes. Moreover, we
consider three different small frequency separations involving, respectively,
modes of degree l = 0, 1, 2, 3; l = 0, 1; and l = 0, 2, and show that they are
all significantly affected by the sharp sound speed variation at the edge of
the core. In particular, we confirm that the frequency derivative of the
diagnostic tool that combines modes of degree up to 3 can potentially be used
to infer directly the amplitude of the relative sound speed variation at the
edge of the core. Concerning the other two diagnostic tools, we show that at
high frequencies they can be up to a few microhertzs smaller than what would be
expected in the absence of the rapid structural variation at the edge of the
core. Also, we show that the absolute values of their frequency derivatives are
significantly increased, in a manner that is strongly dependent on stellar age.
