  We define a subclass of quasiregular curves, called signed quasiregular
curves, which contains holomorphic curves and quasiregular mappings. As our
main result, we prove a growth theorem of Bonk-Heinonen type for signed
quasiregular curves. To obtain our main result, we prove that signed
quasiregular curves satisfy a weak reverse H\"older inequality and that this
weak reverse H\"older inequality implies the main result. We also obtain higher
integrability for signed quasiregular curves. Further, we prove a cohomological
value distribution result for signed quasiregular curves by using our main
result and equidistribution.
