  AQ Men is a nova-like variable which is presumed to have a tilted, precessing
accretion disc. Grazing eclipses in this system have been speculated to be
useful in exploring the geometry of its accretion disc. In this work we
analysed TESS observations of AQ Men, which provide the best light curve of
this object thus far. We show that the depths of the eclipses are changing with
the orientation of the accretion disc, which means that they can serve as a
direct test of the tilted accretion disc models. The precession period of the
accretion disc is increasing during the TESS observations. However, it is still
shorter than the period determined in the previous studies. The amplitude of
the variability related to the precession of the accretion disc varies, and so
does the shape of this variability. Moreover, we have detected a positive
superhump that was previously unseen in AQ Men. Interestingly, the positive
superhump has a strongly non-sinusoidal shape, which is not expected for a
nova-like variable.

Solar and Stellar Astrophysics;High Energy Astrophysical Phenomena