KIC 6951642: confirmed Kepler $\gamma$ Doradus-$\delta$ Scuti star with intermediate to fast rotation in a possible single-lined binary system

KIC 6951642 has been reported as a candidate hybrid pulsator of type-$\gamma$ Doradus-$\delta$ Scuti from observations of the first quarters of the Kepler mission. We aim to investigate the pulsating nature of KIC 6951642 and to search for the signature of rotation and/or activity in the light curves. We performed an iterative frequency search of both Fourier spectra, and searched for regular patterns in them. We applied spectrum synthesis to determine the atmospheric stellar parameters. Since KIC 6951642 was reported to belong to a spectroscopic binary system, we fitted the time delays derived from the light curves with the radial velocities obtained from published as well as new spectra in an attempt to improve the quality of the first orbit. Follow-up spectroscopy showed that KIC 6951642 is a fast-rotating F0-type star in a possible single-lined binary with a period of $\sim$4.8 yr. In the low-frequency regime, we identified the frequencies of 0.721 d$^{-1}$ as well as of 0.0087 d$^{-1}$. We attribute the first frequency to stellar rotation and the second one to stellar activity with a cycle. We also detected $g$ modes, with the strongest mode located at 2.238 d$^{-1}$, as well as three asymmetric multiplets (with a mean spacing of 0.675$\pm$0.044 d$^{-1}$). In the high-frequency regime, we detected frequencies of type-$\delta$ Scuti, with the strongest mode located at 13.96 d$^{-1}$, as well as seven asymmetric multiplets (with a mean spacing of 0.665$\pm$0.084 d$^{-1}$). We subsequently identified a few more frequencies that appear to be combinations of a $g$ or $p$ mode and one of the higher cited frequencies not due to pulsations. We propose that KIC 6951642 accommodates for a fast-rotating $\gamma$ Dor-$\delta$ Sct hybrid star with various rotationally split multiplets of $g$ and $p$ modes and that it also displays a cycle lasting years of (possible) stellar activity