  We present optical photometry and spectroscopy of the afterglow and host
galaxy of gamma-ray burst 040924. This GRB had a rather short duration of T90
~2.4s, and a well sampled optical afterglow light curve. We aim to use this
dataset to find further evidence that this burst is consistent with a massive
star core-collapse progenitor. We combine the afterglow data reported here with
data taken from the literature and compare the host properties with survey
data. We find that the global behaviour of the optical afterglow is well fit by
a broken power-law, with a break at ~0.03 days. We determine the redshift z =
0.858 +/- 0.001 from the detected emission lines in our spectrum. Using the
spectrum and photometry we derive global properties of the host, showing it to
have similar properties to long GRB hosts. We detect the [Ne III] emission line
in the spectrum, and compare the fluxes of this line of a sample of 15 long GRB
host galaxies with survey data, showing the long GRB hosts to be comparable to
local metal-poor emission line galaxies in their [Ne III] emission. We fit the
supernova bump accompanying this burst, and find that it is similar to other
long GRB supernova bumps, but fainter. All properties of GRB 040924 are
consistent with an origin in the core-collapse of a massive star: the
supernova, the spectrum and SED of the host and the afterglow.
