A recent paper of Totaro develops a theory of $q$-ample bundles in
characteristic 0. Specifically, a line bundle $L$ on $X$ is $q$-ample if for
every coherent sheaf $\mathcal{F}$ on $X$, there exists an integer $m_0$ such
that $m\geq m_0$ implies $H^i(X,\mathcal{F}\otimes \mathcal{O}(mL))=0$ for
$i>q$. We show that a line bundle $L$ on a complex projective scheme $X$ is
$q$-ample if and only if the restriction of $L$ to its augmented base locus is
$q$-ample. In particular, when $X$ is a variety and $L$ is big but fails to be
$q$-ample, then there exists a codimension 1 subscheme $D$ of $X$ such that the
restriction of $L$ to $D$ is not $q$-ample.